The cup signifies Jesus' blood of the covenant, poured out for many.

²⁷And he took the cup, and gave thanks, and gave it to them, saying, Drink ye all of it;

²⁸For this is my blood of the new testament, which is shed for many for the remission of sins.

²³And he took the cup, and when he had given thanks, he gave it to them: and they all drank of it.

²⁴And he said unto them, This is my blood of the new testament, which is shed for many.