In classical sacrifices, the people get the good bits, and the gods get the refuse, the bits that would get thrown out otherwise.
Not our God. Leviticus (particularly Leviticus 3) describes the sacrifices that our LORD demanded from His people of Israel. God gets the kidneys, the tail, and all the fat. He gets the prime steak, He gets the best.
Today we do not literally give sacrifices of animals. For us the ultimate sacrifice has been made through our Lord, Christ Jesus. But should always be our ambition to do the same thing - to offer God the best of what we have, to offer Him the fat, and not the smoke and bones.