1 Corinthians 10:16

The cup of blessing which we bless, is it not. communion of the blood of Christ? The bread which we break, is it not. communion of the body of Christ?

'cup of blessing' -the fruit of the vine in the Lord's Supper.

'which we bless' -(1 Corinthians 11:24) 'Over which we pronounce. blessing as by Christ at the institution of the ordinance.' (Robertson p. 154)

The Cup is here mentioned first, because Paul wishes to expand upon the bread and draw an argument from it.

'communion' -2842. koinonia koy-nohn-ee'-ah; from 2844; partnership, i.e. (literally) participation, or (social) intercourse, or (pecuniary) benefaction: -(to) communicate(-ation), communion, (contri-)distribution, fellowship.

'of the blood of Christ' -'lit.,. participation in..the blood of Christ.' (Robertson p. 154)

When Christians partake of the Lord's Supper, they are demonstrating that they share and enjoy the benefits of Christ's death. 'Since, therefore, the cup is specifically interpreted by the Lord (cf. Mark 14:24), and continued to be so understood in the early church (1 Corinthians 11:25), as "my blood of the new covenant), this language almost certainly refers to their sharing in the provisions and benefits of that covenant.' (Fee p. 468)

Point to Note:

Partaking of the Lord's Supper doesn't impart the forgiveness of sins, rather, it is something that forgiven people (i.e. those who already have contact with the blood of Christ) have the right to share in. (Acts 2:41)

'The bread which we break' -(Acts 20:7)