A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
lev 3:1THE PEACE OFFERING OF THE HERD. (Lev. 3:1-17)
if his oblation be a sacrifice of peace offering--"Peace" being used in Scripture to denote prosperity and happiness generally, a peace offering was a voluntary tribute of gratitude for health or other benefits. In this view it was eucharistic, being a token of thanksgiving for benefits already received, or it was sometimes votive, presented in prayer for benefits wished for in the future.
of the herd--This kind of offering being of a festive character, either male or female, if without blemish, might be used, as both of them were equally good for food, and, if the circumstances of the offerer allowed it, it might be a calf.
lev 3:2he shall lay his hand upon the head of his offering--Having performed this significant act, he killed it before the door of the tabernacle, and the priests sprinkled the blood round about upon the altar.
lev 3:3he shall offer of the sacrifice of the peace offering--The peace offering differed from the oblations formerly mentioned in this respect: while the burnt offering was wholly consumed on the altar, and the freewill offering was partly consumed and partly assigned to the priests; in this offering the fat alone was burnt; only a small part was allotted to the priests while the rest was granted to the offerer and his friends, thus forming a sacred feast of which the Lord, His priests, and people conjointly partook, and which was symbolical of the spiritual feast, the sacred communion which, through Christ, the great peace offering, believers enjoy. (See further on Lev 19:5-8; Lev 22:21).
the fat that covereth the inwards--that is, the web work that presents itself first to the eye on opening the belly of a cow.
the fat . . . upon the inwards--adhering to the intestines, but easily removable from them; or, according to some, that which was next the ventricle.
lev 3:4the two kidneys . . . of the flock . . . the whole rump--There is, in Eastern countries, a species of sheep the tails of which are not less than four feet and a half in length. These tails are of a substance between fat and marrow. A sheep of this kind weighs sixty or seventy English pounds weight, of which the tail usually weighs fifteen pounds and upwards. This species is by far the most numerous in Arabia, Syria, and Palestine, and, forming probably a large portion in the flocks of the Israelites, it seems to have been the kind that usually bled on the Jewish altars. The extraordinary size and deliciousness of their tails give additional importance to this law. To command by an express law the tail of a certain sheep to be offered in sacrifice to God, might well surprise us; but the wonder ceases, when we are told of those broad-tailed Eastern sheep, and of the extreme delicacy of that part which was so particularly specified in the statute [PAXTON].
lev 3:12if his offering be a goat--Whether this or any of the other two animals were chosen, the same general directions were to be followed in the ceremony of offering.
lev 3:17ye eat neither fat nor blood--The details given above distinctly define the fat in animals which was not to be eaten, so that all the rest, whatever adhered to other parts, or was intermixed with them, might be used. The prohibition of blood rested on a different foundation, being intended to preserve their reverence for the Messiah, who was to shed His blood as an stoning sacrifice for the sins of the world [BROWN].