Charles Ellicott Commentary Exodus 29:13

"And thou shalt take all the fat that covereth the inwards, and the caul upon the liver, and the two kidneys, and the fat that is upon them, and burn them upon the altar." — Exodus 29:13 (ASV)

You shall take all the fat that covers the inwards. — Whole burnt offerings were, comparatively speaking, rare in the ancient world.

Usually, only parts of the victims were consumed by fire on the altar; the greater portion was either eaten by the priests and the worshippers, or burnt elsewhere than on the altar.

Among the parts regarded as most fitting to be consumed on the altar, the fat always held a high place. This can be accounted for either by its being considered a delicacy, or by the readiness with which it caught fire and kindled into a clear bright blaze.

The caul that is above the liver — i.e., the membrane which covers the upper portion of the liver, sometimes called “the little omentum.”