"While the Hebrew word beriyt (pronounced bear-reet) means "covenant," the cultural background of the word is helpful in understanding its full meaning. Beriyt comes from the parent root word bar meaning grain. Grains were fed to livestock to fatten them up to prepare them for the slaughter.
Two other Hebrew words related to beriyt and also derived from the parent root bar can help understand the meaning of beriyt. The word beriy means fat and barut means meat. Notice the common theme with beriy and barut, they have to do with the slaughtering of livestock.
The word beriyt is literally the animal that is slaughtered for the covenant ceremony. The phrase "make a covenant" is found thirteen times in the Hebrew Bible. In the Hebrew text this phrase is "karat beriyt". The word karat literally means "to cut".
When a covenant is made a fattened animal is cut into pieces and laid out on the ground. Each party of the covenant then passes through the pieces signifying that if one of the parties fails to meet the agreement then the other has the right to do to the other what they did to the animal (see Genesis 15:10 and Jeremiah 34:18-20)."