covenant: a solemn, binding agreement that ties two parties together with obligations, sealed by an oath and meant to hold.
This is the great relational word of the Hebrew Bible. A covenant is a formal bond deliberately entered into, not a tie of blood or chance but one that is chosen and sworn. It binds the parties to obligations, it is normally backed by an oath, and it usually carries a sign or a witness so that it can be remembered: the rainbow, the circumcision, the tablets, the blood splashed on the people, a heap of stones, even a meal of salt.
The word covers a wide range, but the range is held together by one idea, the way the English word "contract" covers everything from a marriage to a peace treaty to a business deal. A covenant can run between equals, where each side pledges loyalty, or it can run from a greater party to a lesser one, where the stronger imposes terms or freely grants a promise. The text uses the same word for an alliance between kings, a pact of friendship between two men, a marriage, a king's deal with his people, and above all the bond between God and Israel.
When God is one of the parties the covenant takes on its deepest weight. Sometimes God binds himself by a promise that asks nothing back, as with Noah and the whole earth, or with Abraham and his offspring. Sometimes God lays obligations on the people and warns of consequences for breaking them, as at Sinai. And the prophets look ahead to a renewed covenant, written not on stone but on the heart. These are not different words but different shapes of the one bond.
Because the word is so flexible, no single English term fits every use, and the safest guide in any verse is not the word alone but what is done with it: how the covenant is made, what sign goes with it, who is bound, and what happens if it is broken.