"The fat that covereth the inwards" refers to the caul or transparent membrane which has upon it a network of fatty tissue: "the fat upon the inwards" refers to the small lumps of suet found upon the intestines of healthy animals.

The fat that covereth the inwards - The omentum, caul or web, as some term it. The fat that is upon the inwards; probably the mesentery or fatty part of the substance which connects the convolutions of the alimentary canal or small intestines.

And he shall offer of the sacrifice of the peace offering,.... That is, the priest, not all of it, but some of it, even what is after mentioned:

an offering made by fire unto the Lord; for what was offered to the Lord was burnt, and is that part of it which is next mentioned in this and the following verse:

the fat that covereth the inwards, and all the fat that is upon the inwards; both that which covered them, and that which stuck to them; and the fat being the best, it was the Lord's, and offered to him, and denoted Christ the fatted calf, whose sacrifice is best and most excellent; and which was typified by that which Abel offered up, and which being of the fat of the flock, and offered up by faith in Christ's sacrifice, was more excellent than Cain's, Genesis 4:4.

The person presenting the sacrifice was to offer as a firing for Jehovah, first, "the fat which covered the entrails" (Leviticus 1:9), i.e., the large net which stretches from the stomach over the bowels and completely envelopes the latter, and which is only met with in the case of men and the mammalia generally, and in the ruminant animals abounds with fat; secondly, "all the fat on the entrails," i.e., the fat attached to the intestines, which could easily be peeled off; thirdly, "the two kidneys, and the fat upon them (and) that upon the loins (הכּסלים), i.e., upon the inner muscles of the loins, or in the region of the kidneys; and fourthly, "the net upon the liver." The net (היּתרת) upon (על Leviticus 3:4, Leviticus 3:10, Leviticus 3:15; Leviticus 4:9; Leviticus 7:4; Exodus 29:13), or from (מן Leviticus 9:10), or of the liver (Leviticus 8:16, Leviticus 8:25; Leviticus 9:19; Exodus 29:22), cannot be the large lobe of the liver, ὁ λοβὸς τοῦ ἥπατος (lxx), because this is part of the liver itself, and does not lie על־כּבד over (upon) the liver; nor is it simply a portion of fat, but the small net (omentum minus), the liver-net, or stomach-net (recticulum jecoris; Vulg., Luth., De Wette, and Knobel), which commences at the division between the right and left lobes of the liver, and stretches on the one side across the stomach, and on the other to the region of the kidneys. Hence the clause, "on the kidneys (i.e., by them, as far as it reaches) shall he take it away." This smaller net is delicate, but not so fat as the larger net; though it still forms part of the fat portions. The word יתרת, which only occurs in the passages quoted, is to be explained from the Arabic and Ethiopic (to stretch over, to stretch out), whence also the words יתר a cord (Judges 16:7; Psalm 11:2), and מיתר the bow-string (Psalm 21:13) or extended tent-ropes (Exodus 35:18), are derived. The four portions mentioned comprehended all the separable fat in the inside of the sacrificial animal. Hence they were also designated "all the fat" of the sacrifice (Leviticus 3:16; Leviticus 4:8, Leviticus 4:19, Leviticus 4:26, Leviticus 4:31, Leviticus 4:35; Leviticus 7:3), or briefly "the fat" (החלב Leviticus 3:9; Leviticus 7:33; Leviticus 16:25; Leviticus 17:6; Numbers 18:17), "the fat portions" (החלבים Leviticus 6:5; Leviticus 8:26; Leviticus 9:19-20, Leviticus 9:24; Leviticus 10:15).

And he shall {b} offer of the sacrifice of the peace offering an offering made by fire unto the LORD; the fat that covereth the inwards, and all the fat that is upon the inwards,

(b) One part was burnt, another was to the priests, and the third to him that offered.

fat: or, suet

3. he 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 Le 19:5-8; 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.

3:1-5 The peace-offerings had regard to God as the giver of all good things. These were divided between the altar, the priest, and the owner. They were called peace-offering, because in them God and his people did, as it were, feast together, in token of friendship. The peace-offerings were offered by way of supplication. If a man were in pursuit of any mercy, he would add a peace-offering to his prayer for it. Christ is our Peace, our Peace-offering; for through him alone it is that we can obtain an answer of peace to our prayers. Or, the peace-offering was offered by way of thanksgiving for some mercy received. We must offer to God the sacrifice of praise continually, by Christ our Peace; and then this shall please the Lord better than an ox or bullock.