The covenant for the Jewish people was expressed in the words: "I will be your God and you will be my people." It was a blood covenant:
Moses took half of the blood and put it in large bowls; the other half he splashed on the altar [representing God]. Taking the book of the covenant, he read it aloud to the people, who answered, "All that the Lord has said, we will heed and do." Then he took the blood and sprinkled it on the people, saying, "This is the blood of the covenant which the Lord has made with you." (Exodus 24:6-8)
All this lies behind the words of Jesus at the Last Supper when he says, "This cup is the new covenant in my blood, which will be shed for you." All this lies behind the taking of the cup by the faithful at every Mass.