Consider the words of Apostle Paul in describing the Lord’s Supper in 1 Corinthians 10:16-18
Is not the cup of blessing which we bless a sharing in the blood of Christ? Is not the bread which we break a sharing in the body of Christ? Since there is one bread, we who are many are one body; for we all partake of the one bread. Look at the nation Israel; are not those who eat the sacrifices sharers in the altar?
The central idea here is that just as those who participated in the covenant meals of ancient Israel were united in the religious body of God’s people, so Christians who participate in the Lord’s Supper become one body with Christ and members of the new covenant people of God, which is the Church.
Believers are united together in the blood of Christ, so as to become one body. A union of this kind is properly called koinonia and it is used to describe the union believers have with Christ and with each other in the Lord’s Supper. This fellowship, or communion, is indeed a sacred fellowship because it speaks of the sacred bond that binds God’s people together in community. Covenantal union is not a fusion whereby our individual identities are erased; rather it is a union characterized by faith, hope, and love. The memorial of the mighty acts of redemption inspires our faith, the proclamation of the promises strengthens our hope, and the sharing of the loaf and the cup with thanksgiving exercises our love.
However, the Lord’s Supper can be thought not only as koinonia with Christ, but as an “incorporation into the body of Christ” as Calvin states it. Consider the words of Calvin in commenting on this passage
But I would ask, what is the source of that koinonia or communion, which exists among us, but from the fact that we are united to Christ so that ‘we are flesh of His flesh, and bone of His bones’… For it is necessary for us to be incorporated, as it were, into Christ in order to be united to each other. Besides, Paul is discussing here not a mere human fellowship, but the spiritual union between Christ and believers… Therefore from the context of this verse, we can conclude that koinonia or communion of the blood is the alliance which we have with the blood of Christ when He ingrafts all of us into His body so that He may live in us, and we are in Him. Commentary on 1 Cor. 10:16, Commentary on First Corinthians, p. 216.
Using the Johannine phrase, “that He may live in us and we in Him” (likely a reference to 1 John 4:13), Calvin sees the sacramental union as both a fellowship and an incorporation.
“Incorporation into the body of Christ” is a very particular image for our communion with Christ. For the Christian, the love of Christ for the Church creates the bond which unites the Church to Himself and it serves as the example for all other social relationships. From a human viewpoint, the most sacred social relationship is the marital union. According to Calvin, the fact that Eve was made of the substance of Adam is significant, since she is “bone of His bone and flesh of His flesh”. Calvin connects this concept to the Lord’s Supper
As Eve was formed out of the substance of her husband Adam, and thus was a part of him, so if we are to be true members of Christ, we grow into one Body by the communication of His substance. In short, Paul describes our union to Christ, a symbol and pledge of which is given to us in the Holy Supper. Hughes Oliphant Old, Holy Communion in the Piety of the Reformed Church, p. 61.
What is the “substance” that is communicated to us? This substance is the new life of the Kingdom of God and it can be spoken of in three ways: as life (i.e. the life of a new humanity in fellowship with God), as light (i.e. the illumination of the inner witness of the Holy Spirit), and as power (i.e. the power which makes us able to do the works of God and nourishes us to eternal life). This is the substance and reality of Christ which is communicated to us by means of the Supper. These blessings of the new covenant are communicated to us, by faith, when we participate in the Supper. The bread and wine given at the Supper are the sign and seal of this substance, which is given to those who receive them in faith. In this sense the Lord’s Supper is not merely a commemoration of Christ’s saving death but a communication of it as well.
As we receive the Supper on the Lord’s Day, may we ponder the blessings that have been secured for us and may we receive from His fullness by faith.