Charles Ellicott Commentary Leviticus 3:3

"And he shall offer of the sacrifice of peace-offerings an offering made by fire unto Jehovah; the fat that covereth the inwards, and all the fat that is upon the inwards," — Leviticus 3:3 (ASV)

And he shall offer. —That is, he who brings the sacrifices, not the priest.

The fat. —That is, the best or choicest part. Hence the expression is also used for the best produce of the ground (Genesis 45:18; Numbers 18:12). As the most valuable part of the animal, the fat belonged to God, and hence had a peculiar sanctity, for which reason it was not allowed to be eaten (Leviticus 3:17; Leviticus 7:23).