From First Corinthians by George T. Montague, SM, commenting on I Corinthians 10:16-17
The union effected by the blood and the body of Christ is a participation. This Greek term koinōnia has a richness difficult to express in a single word. The NAB, RSV, and NIV translate it as “participation.” Others translate it “sharing “(NJB, NRSV) or “communion” (JB). In documents contemporary with Paul, koinōnia is a favorite expression for the marital relationship as being the most intimate between human beings.
Depending on the structure of the Greek, it can mean union with a person, as Paul has already in this letter spoken of a koinōnia with the Son of God (1:9), or a common sharing in something, such as in the faith (Philem 6), in sufferings (Phil 3:10), or in a work of service (2 Cor 8:4). Both senses converge in the koinōnia of the Holy Spirit (2 Cor 13:13).
The term can also stand for the community created by the sharing. All of these senses can be seen in Paul’s use of the word here. The koinōnia of the Eucharist is (1) a common sharing or participation in the body and blood of Christ; (2) an intimate union with the person of Christ; (3) a “community” brought about by the Eucharist, as will be specified in verse 17.
Is the Eucharist a simple meal, or is it also a sacrificial meal? The separate consecration of cup and bread, one signifying the blood and the other the body, certainly points to sacrifice, since the separation of the animal’s blood from its body was essential to sacrifice. In addition, the comparison of the Eucharist with the pagan sacrifices suggests that Paul is saying, “We have our own sacrifice.”