This is the fifth post on sacraments in my ongoing series, theology in bullet points. The first unit in this series had to do with God and Creation (book here), and the second unit was on Christology and Atonement.
We are now in the third and final unit: The Holy Spirit and the Church. The first set of posts in this final unit was on the Holy Spirit. The second set was on the Church. This third set is on sacraments.
Christians vary some in their perspectives on communion.
1. The precise nature of communion was one of the early debate points in the Protestant Reformation. Indeed, disagreement over communion may have ensured that Protestantism would never be a unified church over and against the Roman Catholic Church. In 1529 at the so called Marburg Colloquy, Martin Luther met with another key "protestant" named Huldrych Zwingli. Although they could agree on most items, they did not agree on communion, and this fact was a deal breaker.
Both disagreed, of course, with the Roman Catholic Church's sense of transubstantiation. Transubstantiation is the belief that the bread and wine of communion literally become the body and blood of Christ in communion. It is an idea that reached its maturity with Thomas Aquinas in the 1200s.
It is also an idea, it would seem, that is strongly based in Aristotle's view of reality as a matter of form and substance. The form is all that we can see. The underlying substance is not available to our view.
This perspective, while no longer one we share, did allow transubstantiation to survive into the Age of Science. Even when it could be determined that bread and wine do not physically transform into flesh and blood, the Catholic Church could see the transformation on the level of some unseen substance. There is thus no need for the bread and wine of communion to take on the cell structure of skin, hemoglobin, or platelets. These are the form, whereas it is the substance that literally becomes the body and blood of Christ.
While it is hard to come up with an objection to this belief, it is also difficult to come up with any reason to hold it other than tradition. No one today would retain Aristotle's view of reality in any straightforward way. And no biblical text has such a view, not when properly interpreted. 
2. Luther's own view was far more suitable for a world after Aristotle. Translating transubstantiation into his own view of the world, Luther believed that the "real presence" of Jesus was there in the elements of communion after they were consecrated.  His view is called "consubstantiation."
Again, it is difficult to find any serious objection to this view. Nor can we find any necessity of believing it. It would seem to fall into the category of "disputable issues," and what one believes can be a matter of individual conviction.
3. Zwingli's position is usually associated with a "memorialist" view.  In its extreme form, it sees communion merely as a remembering of Jesus' death and his Last Supper. This view thus seems to undersell the power of communion and the way God uses it to renew and spiritually empower those who come to the table in faith.
All traditions view communion as a memorial, but many see it as more than a mere memorial.
4. In Romans, Paul speaks of the spiritual significance of food. "Nothing is unclean in itself; but it is unclean for anyone who thinks it unclean" (Rom. 14:14). We might say the same of communion. The bread and wine are not intrinsically effective to empower, but to those who are truly and earnestly seeking God's grace, they can facilitate a great moment of spiritual empowerment.
John Calvin suggested that the partaker of communion was taken into the presence of Christ, not that the presence of Christ came to the bread.  However, we need not know such particulars. It is clear that many people experience Christ in communion and that they are empowered in the process.
To the one who has faith, to the one who does truly and earnestly repent of his or her sins, communion is a means of grace. It is a divinely appointed meeting place where, in a sacred moment, God's Spirit renews and empowers us to continue to walk in the Spirit. That is all we need to know.
Next Sunday: SA6: The Scriptures are a sacrament of God's transformation.
 A statement like, "This is my body," could be either literal or metaphorical. Given that Jesus was speaking of bread, the most natural way to take his words is metaphorical, that the bread in some way was like his body.
 The dominant philosophical force in Luther's world was nominalism rather than the metaphysics of Aristotle. In nominalism, things neither have some underlying universal substance (Aristotle) nor are they the material versions of ideas (Plato). Rather, each thing can have its own unique, independent existence and identity unconnected to the existence and identity of other things.
 In reality, Zwingli did in the end use some language of a spiritual presence in communion.
 In this way he avoided the objection of Zwingli and others that Jesus as truly human could not be present in more than one place at once.