Leviticus 3 is giving the requirements and procedures for the peace offerings: first generally “of the herd”, vs1-6, then vs7-11 lambs, and vs12-16 goats. There is some repetition as the requirements and procedures for each class is effectually the same. One would have to be an experienced butcher or hunter to grasp some of this. The respective animal’s physiologies differ slightly. But generally the fat and the blood are given the same treatment. Here is what is said of the lamb: 8 And he shall lay his hand upon the head of his offering, and kill it before the tabernacle of the congregation: and Aaron's sons shall sprinkle the blood thereof round about upon the altar. 9 And he shall offer of the sacrifice of the peace offering an offering made by fire unto the LORD; the fat thereof, and the whole rump, it shall he take off hard by the backbone; and the fat that covereth the inwards, and all the fat that is upon the inwards, 10 And the two kidneys, and the fat that is upon them, which is by the flanks, and the caul above the liver, with the kidneys, it shall he take away. 11 And the priest shall burn it upon the altar: it is the food of the offering made by fire unto the LORD." The blood is sprinkled around the Alter, and the specified fat is burnt upon the Alter. “Food of the offering made by fire” is an interesting phrase. It is repeated in v16 right before your verse, and the words “for a sweet savor: all the fat is the LORD's.” are added to it. Now the without blemish, the coming to the Tabernacle door, the laying of the hands upon its head, and all the other details are very important in their typical depictions of the true Lamb of God that takes away the sin of the world. He is our peace. It is interesting that sweet savor is attached to the burnt fat. Fat generally is abundance as in fat valleys and fields. So is fatty visceral fat, stored up abundance. Given as the sweet savor of the food of the offering by fire, it is prohibited to man. Man has nothing to do with this. It belongs to God.
All meats have fat in them, but the fat here specified are special tissue accumulations around the viscera and removed by the butcher in our processed meats today and by the priests of the tabernacle at that time. Not for human consumption at that time because Christ offered himself to God. As with the blood, so it is with the fat. And thus the prohibition of verse 17 placed upon the covenant people: “It shall be a perpetual statute for your generations throughout all your dwellings, that ye eat neither fat nor blood.”
This behavior was to be a testimony to the law of the offerings and in a larger sense to the atonement of Christ. The ceremonial aspects of the prohibition have nothing to do with any thing else. I sure hope this helps some. …DGB