"Communion" is a term applied to the Lord's Supper because of its usage in 1 Corinthians 10:16. This act of worship emphasizes the fellowship (koinonia — sharing, participation) we enjoy with Christ when we partake of the sacred elements (cf. "with you" in Mt. 26:29).
The communion involves two elements -- "bread" and "fruit of the vine" (Mt. 26:26-29 -- not "water," as per Mormon doctrine).
It is a celebration "in remembrance" of the body and blood of the Savior (Lk. 22:19; 1 Cor. 11:25). The idea that the actual flesh and blood of Christ is present in the elements (transubstantiation -- Catholic dogma; consubstantiation -- Lutheran doctrine) is a human tradition of post-apostolic development.
The communion is authorized only for those who have submitted to the conditions of the new birth (Jn. 3:3-5), hence, are in Christ's kingdom (Mt. 26:29; Lk. 22:29-30).
Christians are to observe the supper each Lord's day. Note the expression "every first day of the week" (1 Cor. 16:2 NASB, et al.), combined with the purpose phrase "to break bread" in Acts 20:7.
There is an intimate connection between Christ's death, represented by the elements, and his resurrection, which occurred on Sunday (see Mt. 28:1; Mk. 16:2; Lk. 24:1; Jn. 20:1). Random communion at other times lacks the authority of the Scriptures.
