A Peace Offering of Sheep (Leviticus 3:6-11).
‘And if his oblation for a sacrifice of peace-offerings to Yahweh be of the flock, male or female, he shall offer it without blemish.
The same instructions are given concerning the offering of the sheep, and then of the goat. This distinction between sheep and goat (contrast chapter 1) may be because in the case of the sheep its fat tail had to be dealt with separately. Or it may be in order to preserve threeness (just as there were three differing offerings mentioned in chapter 1), to indicate the completeness of the sacrifice. The idea may be that however different people are, (farmers, shepherds, goatherds) the ultimate way to God is the same for them all, through sacrifice and making peace with God. For us, and ultimately for them, it is through the unblemished lamb (John 1:29; 1 Peter 1:18-19). There is no other way (John 14:6).
‘If he offer a lamb for his oblation, then shall he offer it before Yahweh, and he shall lay his hand on the head of his oblation, and kill it before the tent of meeting, and Aaron's sons shall sprinkle its blood on the altar round about. And he shall offer of the sacrifice of peace-offerings an offering made by fire to Yahweh; its fat, the fat tail entire, he shall take away hard by the backbone; and the fat that covers the innards, and all the fat that is on the innards, and the two kidneys, and the fat that is on them, which is by the loins, and the covering of fat on the liver, with the kidneys, shall he take away. And the priest shall burn it on the altar: it is the food of the offering made by fire to Yahweh.'
The same principles apply here as for the sacrifice of the ox, except that special attention is drawn to the fat tail of the Near Eastern sheep. This luxury along with all the fat was to be burned on the altar along with all that constituted the life force of the lamb. For the life and the fat was God's. He gave it, and He has taken it away (compare Genesis 7:17).
“It is the food of the offering made by fire to Yahweh.” Note the change from ‘a pleasing odour to Yahweh'. The sacrifice offered in loving obedience is all that He needs to satisfy Him as He joins in fellowship with His own. Note that it is consumed in the flames. God is not seen as feeding on it directly. His ‘food' is the pleasing odour, His spiritual satisfaction in the offering. He partakes of their obedience, love and gratitude.