There are two main parts: 1) Holy Communion is communion with Christ and 2) Holy Communion is communion with the church.
The Anglican doctrine affirms that we participate in the Body and Blood of Christ in Holy Communion:
Then shall the Priest, kneeling down at the Lord's Table, say in the name of all them that shall receive the Communion this Prayer following.http://www.eskimo.com/~lhowell/bcp1662/communion/index.html
WE do not presume to come to this thy Table, 0 merciful Lord, trusting in our own righteousness, but in thy manifold and great mercies. We are not worthy so much as to gather up the crumbs under thy Table. But thou art the same Lord, whose property is always to have mercy: Grant us therefore, gracious Lord, so to eat the flesh of thy dear Son Jesus Christ, and to drink his blood, that our sinful bodies may be made clean by his body, and our souls washed through his most precious blood, and that we may evermore dwell in him, and he in us. Amen.
The Second Book of Homilies, "Of the Worthy Receiving and Reverent Esteeming of the Sacrament of the Body and Blood of Christ":
But thus much we must be sure to hold, that in the Supper of the Lord, there is no vain ceremony, no bare sign, no untrue figure of a thing absent (Matthew 26:26): But (as the Scripture says) the table of the Lord, the bread and cup of the Lord, the memory of Christ, the annunciation of his death, yes, the communion of the body and blood of the Lord, in a marvelous incorporation, which by the operation of the Holy Ghost (the very bond of our conjunction with Christ) is through faith wrought in the souls of the faithful, whereby not only their souls live to eternal life, but they surely trust to win their bodies a resurrection to immortality (1 Corinthians 10:16-17). The true understanding of this fruition and union, which is between the body and the head between the true believers and Christ, the ancient catholic fathers, both perceiving themselves, and commending to their people, were not afraid to call this supper, some of them, the salve of immortality and sovereign preservative against death. Others, a divine communion. Others, the sweet delicacies of our Savior, the pledge of eternal health, the defense of faith, the hope of the resurrection. Others, the food of immortality, the healthful grace, and the conservatory to everlasting life. All which sayings both of the Holy Scripture and godly men, truly attributed to this celestial banquet and feast, if we would often call to mind. Oh how would they inflame our hearts to desire the participation of these mysteries, and oftentimes to covet after this bread, continually to thirst for this food? ...http://www.footstoolpublications.com/Homilies/Bk2_SacramentRec15.pdf
Now it followeth to have with this knowledge a sure and constant faith, not only that the death of Christ is available for the redemption of all the world, for the remission of sins, and reconciliation with God the Father: but also that he hath made upon his Cross a full and sufficient sacrifice for thee, a perfect cleansing of thy sins, so that thou acknowledgest no other Saviour, Redeemer, Mediator, Advocate, Intercessor, but Christ only, and that thou mayest say with the Apostle, "that he loved thee, and gave himselfe for thee" (Gal 2:20). For this is to stick fast to Christ's promise made in his Institution, to make Christ thine own, and to apply his merits unto thy self. Herein thou needest no other man's help, no other Sacrifice, or oblation, no sacrificing Priest, no Mass, no means established by man's invention. That Faith is a necessary instrument in all these holy Ceremonies, we may thus assure ourselves, for that as Saint Paul saith, "without Faith it is unpossible to please God" (Hebrews 11:6). "When a great number of the Israelites were overthrowne in the wilderness, Moses, Aaron and Phineas did eat manna, and pleased God, for that they understood" (saith Saint Augustine) the visible meat spiritually (Augustine, In Johan. Hom. 6). Spiritually they hungred it, spiritually they tasted it, that they might be spiritually satisfied. And truely as the bodily meat cannot feed the outward man, unless it be let into a stomach to be digested, which is healthsome and sound: No more can the inward man be fed, except his meat be received into his soul and heart, sound and whole in Faith. Therefore (saith Cyprian), "when we doe these things, we need not to whet our teeth: but with sincere faith we break and divide that whole bread" (Cyprian, De cana Domini). It is well known that the meat we seek for in this Supper, is Spirituall food, the nourishment of our soul, a heavenly refection, and not earthly, an invisible meat, and not bodily, a ghostly substance [i.e. sustenance], and not carnal, so that to think that without Faith we may enioy the eating and drinking thereof, or that that is the fruition of it, is but to dream a gross carnal feeding, basely objecting and binding our selves to the elements and creatures. Whereas by the advice of the Councel of Nicea, we ought to lift up our minds by faith, and leaving these inferior and earthly things, there seek it, where the Sun of Righteousness ever shineth (Council of Nicea, Concilium). Take then this lesson (O thou that art desirous of this Table) of Emissenus a godly Father, that when thou goest up to the reverend Communion, to be satisfied with spiritual meat, thou looke up with faith upon the holy body and blood of thy God, thou marvel with reverence, thou touch it with the mind, thou receive it with the hand of thy heart, and thou take it fully with thy inward man (Eusebius Emissenus, Serm. de Euchar.).
XXVIII. Of the Lord's Supper.http://www.eskimo.com/~lhowell/bcp1662/articles/articles.html#28
The Supper of the Lord is not only a sign of the love that Christians ought to have among themselves, one to another, but rather it is a sacrament of our redemption by Christ's death: insomuch that to such as rightly, worthily, and with faith receive the same, the bread which we break is a partaking of the body of Christ, and likewise the cup of blessing is a partaking of the blood of Christ.
Transubstantiation (or the change of the substance of bread and wine) in the Supper of the Lord, cannot be proved by Holy Writ, but is repugnant to the plain words of Scripture, overthroweth the nature of a Sacrament, and hath given occasion to many superstitions.
The body of Christ is given, taken, and eaten in the Supper, only after an heavenly and spiritual manner. And the mean whereby the body of Christ is received and eaten in the Supper is Faith.
The Sacrament of the Lord's Supper was not by Christ's ordinance reserved, carried about, lifted up, or worshipped.
My emphases in italics and bold font indicate that the classic reformed Anglican doctrine of Holy Communion emphasizes the union between Christ and the Body of Christ, the Church, of which he is the Head, through partaking of his Body and Blood, truly signified by the sacramental bread and wine, of Holy Communion. The emphasis is the gospel truth that God and man have been intimately reconciled to loving, everlasting communion, on the grounds of Christ's death on the cross, by the means of faith, through the power of the Holy Spirit. This is the beautiful mystery of the gospel. And it is in this union that Christ confers the benefits of the Gospel to the faithful; namely, Himself!
But that's not all. There is emphasis on the unity of the church too.
As Article XXVIII affirms, Holy Communion is a sign of the love that Christians have with one another. Recall the apostle's words in 1 Corithians 10. He speaks at pretty great length regarding the divided Corinthian's practices around the Lord's Supper. Paul argues strongly against any idea that suggests that the Lord's Supper is a pagan feast and argues strongly against any idea that one can participate in the Lord's Supper and other pagan feasts and claim exclusive identity among the Body of Christ. Moreover, he urges the Corinthians to exercise caution when eating foods that may cause other Christians consternation. At the heart of his argument lies these statements,
1 Corinthians 10:16-24
The cup of blessing that we bless, is it not a participation in the blood of Christ? The bread that we break, is it not a participation in the body of Christ? Because there is one bread, we who are many are one body, for we all partake of the one bread. Consider the people of Israel: are not those who eat the sacrifices participants in the altar? What do I imply then? That food offered to idols is anything, or that an idol is anything? No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be participants with demons. You cannot drink the cup of the Lord and the cup of demons. You cannot partake of the table of the Lord and the table of demons. Shall we provoke the Lord to jealousy? Are we stronger than he? "All things are lawful," but not all things are helpful. "All things are lawful," but not all things build up. Let no one seek his own good, but the good of his neighbor.
Paul then picks up on the truth of unity again in Ch.11,
1 Corinthians 11:20-29
When you come together, it is not the Lord's supper that you eat. For in eating, each one goes ahead with his own meal. One goes hungry, another gets drunk. What! Do you not have houses to eat and drink in? Or do you despise the church of God and humiliate those who have nothing? What shall I say to you? Shall I commend you in this? No, I will not. For I received from the Lord what I also delivered to you:
that the Lord Jesus on the night when he was betrayed took bread, and when he had given thanks, he broke it, and said, "This is my body which is for you. Do this in remembrance of me." In the same way also he took the cup, after supper, saying, "This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me." For as often as you eat this bread and drink the cup, you proclaim the Lord's death until he comes. Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty of profaning the body and blood of the Lord. Let a person examine himself, then, and so eat of the bread and drink of the cup. For anyone who eats and drinks without discerning the body eats and drinks judgment on himself.
Here Paul criticizes the Corinthian "supper," which sounds more like an "eat-and-run" kind of free for all, with beer on tap, by saying, "You're not eating the Lord's Supper." Notice the problems: disunity (21a), inequitable distribution (22b), drunkenness (21b). These all demonstrate a lack of discernment of the body (29).
Now here is where I want us to pause and think for a minute. What "body" is Paul talking about? I strongly believe that the context must make us understand "body" here to mean the Body of Christ, the church. Some have read this to mean the sacramental bread, such that one should discern something special about it. Given that Paul's corrective instructions for the Corinthians have focussed on their disunity throughout this letter, and especially in these passages, Paul's teaches that the church ought to conform to the reality of it's unity, grounded in the death of Jesus Christ. And what's more, Christians must examine themselves, together as a body and individually to determine what sins may cause disunity in the community of the saints.
Here's how the classic Anglican Book of Common Prayer assists the Church to this end:
DEARLY beloved in the Lord, ye that mind to come to the holy Communion of the Body and Blood of our Saviour Christ, must consider how Saint Paul exhorteth all persons diligently to try and examine themselves, before they presume to eat of that Bread, and drink of that Cup. For as the benefit is great, if with a true penitent heart and lively faith we receive that holy Sacrament; (for then we spiritually eat the flesh of Christ, and drink his blood; then we dwell in Christ, and Christ in us; we are one with Christ, and Christ with us;) so is the danger great, if we receive the same unworthily. For then we are guilty of the Body and Blood of Christ our Saviourhttp://www.eskimo.com/~lhowell/bcp1662/communion/index.html
I purpose, through God's assistance, to administer to all such as shall be religiously and devoutly disposed the most comfortable Sacrament of the Body and Blood of Christ; to be by them received in remembrance of his meritorious Cross and Passion; whereby alone we obtain remission of our sins, and are make partakers of the Kingdom of heaven. Wherefore it is our duty to render most humble and hearty thanks to Almighty God our heavenly Father, for that he hath given his Son our Saviour Jesus Christ, not only to die for us, but also to be our spiritual food and sustenance in that holy Sacrament.http://www.eskimo.com/~lhowell/bcp1662/communion/index.html
Biblical Theology footnote
God delights in eating and drinking with his covenant people. Consider the Mosaic Covenant at Sinai. After Israel receives the covenant from Moses,
Exodus 24:8-11 8 And Moses took the blood and threw it on the people and said, "Behold the blood of the covenant that the LORD has made with you in accordance with all these words." 9 Then Moses and Aaron, Nadab, and Abihu, and seventy of the elders of Israel went up, 10 and they saw the God of Israel. There was under his feet as it were a pavement of sapphire stone, like the very heaven for clearness. 11 And he did not lay his hand on the chief men of the people of Israel; they beheld God, and ate and drank.
Deut 16:5-8 You may not offer the Passover sacrifice within any of your towns that the Lord your God is giving you, but at the place that the Lord your God will choose, to make his name dwell in it, there you shall offer the Passover sacrifice, in the evening at sunset, at the time you came out of Egypt. And you shall cook it and eat it at the place that the Lord your God will choose. And in the morning you shall turn and go to your tents. For six days you shall eat unleavened bread, and on the seventh day there shall be a solemn assembly to the Lord your God. You shall do no work on it.
Consider, of course, the last supper that Jesus spends with his disciples,
Luke 22:15-16 15 And he said to them, "I have earnestly desired to eat this Passover with you before I suffer. 16 For I tell you I will not eat it until it is fulfilled in the kingdom of God."
Consider all the times that Jesus ate and drank with people in their homes (so much so he was accused of being a drunk!),
Luke 14:7-15 7 Now he told a parable to those who were invited, when he noticed how they chose the places of honor, saying to them, 8 "When you are invited by someone to a wedding feast, do not sit down in a place of honor, lest someone more distinguished than you be invited by him, 9 and he who invited you both will come and say to you, 'Give your place to this person,' and then you will begin with shame to take the lowest place. 10 But when you are invited, go and sit in the lowest place, so that when your host comes he may say to you, 'Friend, move up higher.' Then you will be honored in the presence of all who sit at table with you. 11 For everyone who exalts himself will be humbled, and he who humbles himself will be exalted." 12 He said also to the man who had invited him, "When you give a dinner or a banquet, do not invite your friends or your brothers or your relatives or rich neighbors, lest they also invite you in return and you be repaid. 13 But when you give a feast, invite the poor, the crippled, the lame, the blind, 14 and you will be blessed, because they cannot repay you. You will be repaid at the resurrection of the just." 15 When one of those who reclined at table with him heard these things, he said to him, "Blessed is everyone who will eat bread in the kingdom of God!"
And finally consider the promise of the Marriage Supper of the Lamb,
Revelation 19:7-9 7 Let us rejoice and exult and give him the glory, for the marriage of the Lamb has come, and his Bride has made herself ready; 8 it was granted her to clothe herself with fine linen, bright and pure" - for the fine linen is the righteous deeds of the saints. 9 And the angel said to me, "Write this: Blessed are those who are invited to the marriage supper of the Lamb." And he said to me, "These are the true words of God."
I suggest that since we find instances throughout the Bible of banqueting with God, whether in this world or in the world to come, in some sense, Holy Communion should be understood to be part of that great tradition of feasts with God. Moreover, as Passover, which remembered God's deliverance of Israel from the house of salvery, is now endued with new meaning in the Lord's Supper (the deliverance of God's people from slavery to sin and death through the cross), it points us toward the consummation of God's plans for his people in the Kingdom of God in the world to come. Thus, Holy Communion leads us to look in three "directions": (1) we look back to the cross of Christ remembering his death; (2) we look with faith to Christ in the Supper to recieve him now; and (3) we look forward to the consummation of the Kingdom of God and the great marriage supper of the Lamb in which the members of Christ's Body get to participate. We get the whole sense of the Gospel; namely, Christ's work on our behalf in the past, present and future. Christ's work, to which the Lord's Supper points, links the people of God, who now enjoy the eschatological in-breaking of God's Kingdom into this age in the person of Jesus Christ (our communion with Christ), with the promise of the ultimate feast, the Marriage Supper of the Lamb, in the world to come.
Could there be any greater meal for God's people? Could there be any greater enactment of the Gospel that Christians could participate in? Could any evangelical doctrine of Holy Communion be more thorough or biblical? How we need to teach this to Anglicans in the US today.