Leviticus 3:1-5 a sacrifice of peace offering
Most of us think of a peace offering as a gift or gesture intended to repair a breach, to seek for reconciliation, or sue for peace. This is NOT what the text means by a “peace offering.” The translation has been rendered twenty different ways which we need not consider. Think of it as an offering made when you are “at peace” with the Lord, when you feel some confidence in your standing before the Lord. In this respect, it is the opposite of a sin or trespass offering. The sin offering is offered after a mistake or transgression is made, when the petitioner seeks forgiveness from the Lord. What if there has been no sin? The peace offering is offered when no sin or trespass has occurred. The offering is given in thanksgiving or when making a vow.
Let’s say you’re planning a big family get together. You intend to “kill the fatted calf,” as it were, for the feast. In such a situation, it was proper to take your animal to the door of the tabernacle and slay it as a peace offering before the priest, who would take some for himself, and place the fat on the already burning altar for the Lord. In this way, like a prayer of thanks, the priest and the Lord are remembered as participants in the celebration.
“A peace offering in the Old Testament Law is described in Leviticus 7:11–21. It was a voluntary sacrifice given to God in three specific instances. First, a peace offering could be given as a freewill offering, meaning that the worshiper was giving the peace offering as a way to say thank you for God’s unsought generosity. It was basically just a way to praise God for His goodness. The second way a peace offering could be given was alongside a fulfilled vow. A good example of this was when Hannah fulfilled her vow to God by bringing Samuel to the temple; on that occasion she also brought a peace offering to express the peace in her heart toward God concerning her sacrifice—it was a way to say, “I have no resentment; I am holding nothing back in the payment of my vow.” The third purpose of a peace offering was to give thanksgiving for God’s deliverance in an hour of dire need. None of these three reasons to sacrifice had anything to do with propitiation, with appeasing God, or with pacifying Him.” (https://www.gotquestions.org/peace-offering.html)
Leviticus 3:1 the herd; whether it be male or female
The Peace Offering Sacrifice is different than the other sacrifices. It is NOT in similitude of the Only Begotten. The offered animal doesn’t represent the sacrifice of Christ because it is literally “what’s for dinner.” If you are going to kill the fatted calf or dress the dinner lamb, you don’t have to worry about it being a firstborn male, you just have to make sure it came from your herd and not your neighbor’s. Therefore, the animal can be male or female, it doesn’t matter.
“The peace offering is different than other burnt offerings, sin offerings, or trespass offerings. The animal sacrificed in this ordinance does not represent the Messianic sacrifice. Hence, the offering could be male or female, still without blemish, but either gender of cattle, lamb, or goat. One translation calls these well-being offerings, ‘the animal is eaten by the offerer and invited guests as a festival meal in the Lord’s presence.’ Well-being offerings are thus the natural expression of gladness, the worshipper celebrating by feasting in the presence of God in acknowledgment of His loving-kindness.” (The Jewish Study Bible, ed. by A Berlin & MZ Brettler [New York, Oxford University Press, 2nd ed., 2014], 200)
“Both offerer and priest were fed upon that which was not symbolically consumed by God. In this respect it differed from all other offerings. God, man, priest, and even his family were all to partake of this offering and find satisfaction in it. . . Such is the peace enjoyed only by those who can feast together in perfect unity and harmony.” (Joseph Fielding McConkie, Gospel Symbolism [Salt Lake City: Bookcraft, 1999], 89)
Leviticus 3:3-4, 9-10, 14-15 the fat that covereth the inwards. . . and the two kidneys
These verses are the butchering instructions for the offerer or the priests; it’s hard to tell from the text who holds the knife. The instructions differ slightly for cattle, lamb, or goat, respectively. Interestingly, the Lord’s portion is described as the “food of the offering” and was largely made of fat, not the best portion of the animal. The Lord takes the least desirable portion in this example as if to indicate that He just wants the offerer to remember him as the source of all goodness, including the animal offering before him.
Leviticus 3:11 it is the food of the offering made by fire unto the Lord
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.(https://www.cgg.org/index.cfm/library/article/id/809/the-offerings-of-leviticus-part-four-peace-offering.htm)