I'm currently working on an essay called "Re-thinking the Sacraments for the Post-Chrisendom Baptist Church" for a book on Baptists and the Sacraments edited by Anthony Cross (editor at Paternoster). I'm having fun reading, thinking, and praying over 1 Cor. 10.14-22:
14Therefore, my beloved, flee from idolatry. 15I speak as to sensible people; judge for yourselves what I say. 16The 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? 17Because there is one bread, we who are many are one body, for we all partake of the one bread. 18Consider the people of Israel:[a] are not those who eat the sacrifices participants in the altar? 19What do I imply then? That food offered to idols is anything, or that an idol is anything? 20No, I imply that what pagans sacrifice they offer to demons and not to God. I do not want you to be participants with demons. 21You 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. 22Shall we provoke the Lord to jealousy? Are we stronger than he?
What does it mean in v. 16 to have a "participation" or "sharing" in the blood of Christ? Well, I do not think that it means some kind of mystical unity achieved by teh ingestion of the elements as if one were eating the "Lord". The meal creates fellowship between the believer and Christ and, as a corollary, between the believers themselves. The sacrament is not to do with anything in the bread or cup but it pertains to the fellowship one experiences with Christ and the fellowship that one experiences with other Christians. I think there is a sacrament here, but the sacrament is the communing with Christ and communing within the eschatological community of the new covenant. It is also an exclusive communion and because of the covenantal obligation it places upon participants, that communion is not to be shared with others such as the table of pagan deities who are in reality demons.
The participate in the Lord's Supper/Communion/Eurcharist/Jesus-meal (or whatever you want to call it) is to confess that Jesus died and rose and will come again, and by eating and drinking one believes that he is Lord and one belongs to the community that honours Christ's name.