a severed half of an animal, one of a matching pair laid out so people making a covenant could pass between the pieces under a binding oath
This is a rare and highly specialized word. In its everyday sense it simply means a piece cut off something, but the Hebrew Bible keeps it almost entirely for one setting: the ceremony of making a covenant. It comes from a verb meaning to cut in two, and in every place it appears it names the halves of an animal that has been split down the middle for that ceremony.
The ritual behind the word worked like this. An animal was killed and cut in two, and the two halves were set opposite each other with a path between them. The people binding themselves by the agreement then walked down that path between the pieces. The act was a kind of sworn oath in physical form: it said, in effect, may I be cut apart like this animal if I break my word. Covenants like this are found across the ancient world, from treaty texts of surrounding nations, and the same picture lies behind the two biblical scenes where the word occurs.
In Genesis, God makes his promise to Abraham this way, and strikingly it is God alone, appearing as fire, who passes between the pieces, taking the weight of the oath on himself. In Jeremiah, the picture turns to judgment: the people had walked between the halves of a calf to seal a promise to free their slaves, then broke it, so the fate of the cut animal is pronounced over them. Small and uncommon as this word is, it carries the whole force of that sworn, self-binding oath.