We need to understand the order followed here: The offerer brought his offering to the altar, laid his hand on it, and slew it. The priest sprinkled the blood upon the altar and around it. The animal was then cut up, and God's portion—almost entirely fat, besides the two kidneys—was placed on top of the already burning burnt and meal offerings.
Then the priest received the breast and right shoulder for himself and his children, and the offerer received the remainder of the animal to eat. However, it had to be eaten within one day if it was a thank offering or within two days if it was a vow or voluntary offering. If any remained on the third day, it had to be burned. In this process, the major teaching of the peace offering is revealed.
Recall that the burning on the altar of the sweet-savor offerings pictures God consuming a meal and being satisfied. Likewise, the priest receiving his portion shows him being satisfied, and the offerer with his portion is also satisfied. "Filled," "gratified," "contented," "accepted," "convinced," "supplied," "persuaded," "pleased," and "assured" all capture the intent of the symbolism.
In addition, since all parties—God, priest, and man—share the same meal and satisfaction, it shows all in peaceful communion or fellowship. Because it was placed in sequence on top of the other two offerings, the peace offering is directly connected to them, and thus it depicts the effect of perfect devotion to God and man: peaceful satisfaction and fellowship, the fruit of devotedly keeping the two great commandments of the law.
In this sacrifice Christ symbolically plays all three parts: He is the offering, sacrificing His life in service; He is the priest, serving mankind at the altar as Mediator; and He is the offerer, bringing His sacrifice to the altar. The altar, the place of meeting for all three, represents sacrificial services and devotion to God that give Him satisfaction and result in our acceptance.
The peace offering shows man, as Christ, accepted, fed, strengthened, and satisfied by sacrifice, teaching that sacrifice is indeed the essence, the heart and core, the essential element, of love whether to God or man. More specifically, it shows us that sacrifice plays a major role in acceptance before God, spiritual feeding and therefore spiritual strength, and spiritual satisfaction. Devoted people sacrifice for those they love. Thus, sacrifice indicates devotion to God (burnt offering) and devotion in service to man (meal offering).
John W. Ritenbaugh
The Offerings of Leviticus (Part Four): The Peace Offering