In Hebrew thought blood was the seat of life, or even identified with life, and it therefore had an essential role in sacrifices, which were themselves fundamental in Hebrew society. The priests were consecrated by blood (Exod. 29: 19–21); blood sprinkled on the altar expiated sins (Lev. 17: 6); blood dashed over the people established the covenant with the Lord (Exod. 24: 8).
In the NT the blood of Jesus signifies the atoning power of his death. So the obedience of his life and death becomes the basis for the new covenant (1 Cor. 11: 23–9); and the words of Jesus in verse 25, ‘This cup is the new covenant in my blood’, are the oldest record in the NT of what he is doing and explaining at the Last Supper. Paul's account then appends Jesus' injunction that the rite should be repeated, and this became accepted as instruction for the regular celebration of the Church's Eucharist. In Catholic doctrine the wine in the cup, as with the bread, when blessed in the appropriate form by a duly authorized priest or bishop having the right intention, becomes the whole substance of the Body and Blood of Christ, only the appearances (the ‘accidents’) of bread and wine remaining. Other doctrines of the Eucharist, deriving from the Reformation, hold that the word ‘is’ means no more than ‘represents’: the Eucharist is a commemoration of the sacrifice of Christ. But possibly the language (‘is’) is performative rather than descriptive. It changes the status of the bread and the wine. Drinking from the cup of the new covenant is a means of fellowship with the Paschal (Passover) lamb slain for us (1 Cor. 5: 7): and is given by Jesus for his followers to keep in touch with him who died on the cross and who was raised to new life at Easter.