Vayikra 3:17 records that in all places and in all times it is prohibited for a person to eat the helev, fat, of an animal and the blood of the animal. 7:23-25 repeats the prohibition of eating fat and adds more details regarding the prohibition: 7:23 explain that the prohibition is limited to three types of animals, ox (cows), sheep and goats, 7:24 explains that a person can use the fat of a nevelah and a trefah and 7:25 explains that the punishment for transgressing the law is karet. What is the definition of fat? Why is eating fat forbidden?
The Rambam (Laws of Forbidden foods, 7:5, see also Levine, 1989, p. 16) defines the forbidden fat as the fat on the inner organs that relate to the digestive track. This definition is from the context of verse 3:17 within the laws of the shelamim sacrifice, 3:1-16. Within the discussion of the shelamim sacrifice, 3:3,4,9,10,14,15, record that the fat of the kidneys, intestines, liver, stomach(?), from cows, sheep or goats which are offered as shelamim sacrifices is to be burnt on the altar. Thus, as the prohibition of eating fat is recorded at the end of the laws of the shelamim sacrifices, it is reasonable that the prohibition of fat is referring to the fat mentioned by the laws of sacrifices. This connection is strengthened since 7:23-25 explains that the prohibition of eating fat is only by animals that can be offered as a sacrifice, and this implies that the definition of the fat that is prohibited is related to the fat by the sacrifices.
Why is eating fat of cows, sheep and goats prohibited? The Rambam (Moreh 3:48, Maimonides, 1963, p. 598) explains that the prohibition is for health reasons that "the fat of the intestines makes us full, spoils the digestion and produces cold and thick blood." Ignoring the factual question of whether fat is medically bad, it is unlikely that this was the reason for the prohibition. From 7:25, we learn that a person can eat fat from animals that are not able to be sacrificed. Why would the Torah only forbid a person from eating unhealthy fat from some types of animals and not others?
Hoffmann (1953, p. 123, on 3:17, see also Altar, 2004, p. 555) notes that the prohibition of fat has to be related to the sacrifices, and he explains that the prohibition is because what is offered as a sacrifice cannot be eaten as a fear of G-d. Levine (1989, p. 45) varies this slightly. He explains that the prohibition of fat is a gezirah, "a fence around the law. Once the fat of sacrificial animals was forbidden, the fat of all pure animals was forbidden as well, whether or not the animals in question were actually sacrificed." Yet, by the olah sacrifice, the entire animal is sacrificed, and still the meat of animals is permitted to be eaten? Even in reference to the shelamim sacrifice, the kidneys, which are offered on the altar, 3:4,10,15, can be eaten by non-sacrificial meat. Why was there no gezirah by the kidneys? Why was the fat of animals that are sacrificed so important that even the fat by animals that are potential sacrifices but are not brought as sacrifices also forbidden to be eaten?
My guess is that the fat is the crucial part of the shelamim sacrifice, and other sacrifices, while the meat in the sacrifices is incidental. Thus, the shelamim sacrifice was essentially an offering of the fat of the animal as almost no meat except the kidneys was offered on the altar. (Maybe the kidneys were offered due to the difficulty and/ or time needed to remove the fat from them.)
The fat is the crucial part since this is what makes the sacrifice into a smoke (3:5,11,16 and 7:31) and/ or a "fire offering," 3:3,5,9,11,14,16. 6:5 refers to putting wood on the fire but this was just to keep the fire going or to start it, as during the day it was the fat that the was principle combustible item in the sacrifices. The smoke from the fat recalls the image of the cloud of G-d (Shemot 13:21,22) and fire from the fat is the imagery of glory of G-d (Shemot 24:17). Thus, 3:16 records that all the fat is to G-d since the fat is what generated these symbols of G-d. Maybe the imagery was for a person to realize that the sacrifice he/ she was offering was to G-d and not to some demons.
Once fat had this important role by the sacrifices to create an image of the cloud/ fire of G-d, then the Torah instituted a gezirah (“fence”) with regard to the animals that potentially could be brought as sacrifices but were not offered as sacrifices that it was forbidden to eat the fat of these animals. This gezirah was limited in several ways. One, the fat from an animal that could not be brought as a sacrifice since the animal had become a nevelah or a trefah could be used though not eaten, 7:24, and two, the fat of an animal that could not be offered as a sacrifice was permitted to be eaten, i.e. no double gezirah. Finally, even though the oil by the minhah sacrifices (2:1,4-7,15, and Bemidbar 5:15) probably had a similar role in creating smoke and fire by the minhah sacrifice, no gezirah was instituted on all oils, possibly since oil was not intrinsic to the minhah sacrifice unlike the fat which was intrinsic to the animal being sacrificed.