"The less is blessed of the better" (Hebrews 7:7). Aaron and the priests pronounced the benediction (Numbers 6:22-27; Deuteronomy 10:8). Jacob and Moses gave dying blessings prophetical of the character and history of the several tribes (Genesis 49; Deuteronomy 33). The cup in the Lord's supper is called "the cup of blessing" from the Passover cup of wine called so because "blessing" was offered over it to God. 1 Corinthians 10:15.
Paul says, "the cup which WE bless," namely, the minister and the congregation; not he alone by any priestly authority, but as representing the congregation who virtually through Him bless the cup. The celebrant is the church. The minister is the leader of the congregation. The consecration is the corporate act of the whole church. The joint blessing by him and them (not the cup itself, which in the Greek is not nominative but accusative) and the consequent drinking together constitute the "communion," i.e. joint participation of the blood of Christ.