A personal sacrifice
All aspects of the Torah have a lesson to be learned in one’s service of G-d. So too, the concept of burning the fats of the sacrifice atop the altar has a lesson in one’s service of G-d as well. Ramban (Nachmanides) explains that the idea that an animal sacrifice atones for an individual is, since, as the person is bringing his offering he is to think, that in truth, all that is being done with the animal should be done to him. G-d, however, through his kindness, exchanged his life for the life of the animal.
Text 9
It is because man’s deeds (of the sin) are fulfilled through the vehicle of thought, speech and action, that G-d commanded that when a person sins, he should: lean his hands on the animal correlating to action, verbally repent, paralleling speech and he should sacrifice atop the altar the innards and the kidneys, which are the tool of thought and lust... so that man should think when he does all these things, that he sinned towards his G-d with his body and his soul and that it is fitting that his blood be spilled, and his body burnt—were it not for the kindness of the Creator, Who took a substitute [for him]. Ramban, Vayikra 1:9
From his commentary it is understood, that when one burns the fat of the sacrifice on top of the altar, it is representative of the person sacrificing his own pleasures to the Almighty.
Text 10
And the priest shall cause it to [go up in] smoke on the altar, consumed as a fire offering, [with] a pleasing fragrance. All fat belongs to the Lord. Vayikra 3:16
