The term "brit" means "covenant," an obligation or promise with the force of legality behind it. There are two parties to a covenant, and in most cases, both parties shoulder obligations.
The Tana"kh (Hebrew Scripture) knows of covenants solemnified by oaths, sacrifices, ritual meals, and even an elaborate ritual involving the severing of an animal as a demonstration of the consequences befalling any party to the covenant who fails to keep his end of the obligation. The form of such covenants was common in the ancient Near East, however the content of the covenants of the Tana"kh are unique to Jewish tradition. What is more, only Jewish tradition applies the concept of covenant to the relationship between God and people.
Linguists suggest that the etymology of the word "brit" is "bind" or "fetter," which is apt since entering into a covenant binds one to the other party and one's obligations to the other party.
Covenant is the most prominent metaphor describing Israel's relationship with God. In fact, the covenant with Israel is the third covenant enacted by God. First, God made a covenant with all humanity in the aftermath of the Flood in Noah's generation. Then, God promised never again to destroy the world with such a massive and devastating destruction as that wrought by the Flood. The Torah records that the rainbow serves as a sign of this first covenant. Unlike most covenants, the covenant following the Flood was unilateral: God is obligated, but humanity is not. God makes a second covenant with Abraham in which God promises to make Abraham's descendants numerous and to give them the Land of Israel as their possession (Genesis, chapter 17). Abraham signifies his loyalty to God and acceptance of God's covenant through the ritual of circumcision, which not only he undergoes, but all males of his household from the age of eight days; circumcision is the sign of the second covenant. The covenant of Abraham continues in force for all Jews and hence all baby boys are circumcised on the eighth day of life; the ceremony is called "brit milah" meaning "covenant of circumcision." The third covenant is made between God and Israel at Mount Sinai. Here, the Torah which God gives Israel, stipulates the conditions of the covenant. Indeeed, it is the covenant. This third covenant is also distinguished because, as the Torah describes, the entire people Israel stood at the base of Mount Sinai and entered into the covenant at the time the Torah was given. Each year on Shavuot, Jews celebrate the Giving of the Torah at Mount Sinai with a mind toward re-enacting and experiencing this momentous event in our history. The Torah records that Shabbat (the sabbath) is the sign of the third covenant. There is also a fourth covenant in the Tana"kh, between God and King David, in which God gifts David with the Land of Israel and establishes through him a dynasty to rule in perpetuity over Israel (II Samuel 7).
Judaism speaks of the relationship between God and Israel in legalistic terms: We speak of God as the "commander" and Jews as "being commanded by God" to engage in certain behaviors and being prohibited from certain behaviors. We speak of "mitzvot" (commandments), "mishpatim" (statutes), and "chukkim" (ordinances). Whether taken literally or as a metaphor, the notion of covenant permeates every aspect of the God-human relationship: The relationship that binds God to Israel and Israel to God is one of obligation and demands continued loyalty.This model serves as the paradign for human relationships, as well, especially the marital relationship, which is conceived in covenantal terms: A man and woman are obligated to one another in a manner requiring respect, mutuality, and loyalty.