Similar to a business agreement or contract made today, in the ancient Near East, there was a special covenant form in which a greater party (usually a king), established a relationship with a lesser party (a vassal). The greater party determined the responsibilities of each, and the lesser party accepted or rejected the relationship.
God used this kind of covenant when dealing with his people. For example, God made a covenant with Noah (Gen. 9:8-17). God, who controls all nature, promised to never again create a flood that would destroy all earthly life. After the flood, he sent a rainbow as a symbol of this covenant.
God also used this covenant form when he promised to make Abraham the father of a great nation (Gen. 15). God later renewed this covenant with Abraham's descendants, the Israelites, and gave detailed covenant terms through the Ten Commandments and the laws of Leviticus.
Jesus is God's perfect Son and he also makes a covenant with all believers, promising to give us salvation through his sacrifice (Heb. 13:20, 1 Cor. 5:7). The bread and cup today symbolize his broken body and shed blood, reminding Christians that God has faithfully kept the covenant.