In the burnt offering the whole animal goes to the altar. In the purification and reparation offerings the priests eat what the altar does not take. The offering of well being is the only class where the person who brought the animal eats it, and that single fact governs everything else about the rite.
The division is in three parts. The altar receives the fat covering the entrails, the fat on them, the two kidneys with the fat on the loins, and the appendage of the liver, which are burned on top of the burnt offering already lying there. The priests receive the breast, which is elevated, and the right thigh, which is set aside as a due; Leviticus assigns these as a perpetual portion for the priests from the offerings of the people. Everything remaining goes back to the offerer, who takes it away and eats it with family and guests in a state of ritual purity, which means the meal is conditional on the state of everyone at it.
Because meat is eaten there is a clock on it. Thanksgiving flesh must be finished the day it is offered; the flesh of a vow or a freewill offering may be eaten on the second day as well, and anything left on the third is neither eaten nor kept. A person who eats it anyway does not merely waste it; the text says the offering will not be credited to the one who brought it. The class also carries the general prohibitions of the system in their sharpest form, since this is the offering ordinary households handled: no fat and no blood, ever, and no one in a state of impurity may eat any of it.