Leviticus 3
The fellowship offering (shelem, from shalom) is the covenant's most communal offering: unlike the burnt offering that is entirely consumed, the fellowship offering creates a shared meal among God, the priests, and the worshipping household. Cattle, sheep, or goats — male or female — may be offered, making this the most inclusive of the major offerings. In every case the procedure is the same: hand-laying, slaughter, blood-splash on the altar, and the burning of the fat portions and inner organs on God's behalf. The chapter closes with the absolute declaration that all the fat is the Lord's, paired with the prohibition on eating fat or blood — both substances belong to God as the richest portion (fat) and the life-substance (blood) of every animal. The fellowship offering's shared meal is the liturgical form of the covenant relationship: God and His people at table together, each receiving their portion.
Leviticus 3:1
If someone's offering is a fellowship offering, and they offer an animal from the herd, whether male or female, they are to present before the Lord an animal without defect. The fellowship offering — shelem, from the root shalom, peace or wholeness — is the offering of covenant communion: the animal is partly burned on the altar for God, partly given to the priests, and partly eaten by the offerer and their household. Unlike the burnt offering that is entirely consumed, the fellowship offering creates a shared meal. The male-or-female specification (unlike the burnt offering's male-only requirement) and the without defect standard establish the range and the quality of what is acceptable for covenant communion.
Leviticus 3:2
You are to lay your hand on the head of your offering and slaughter it at the entrance to the tent of meeting. Then Aaron's sons the priests shall splash the blood against the sides of the altar. The hand-laying and slaughter at the tent's entrance follow the same pattern as the burnt offering. The offerer identifies with the animal, kills it, and the priests apply the blood to the altar. The blood application that is common to all the major offerings communicates the consistent principle: every approach to God through sacrifice is mediated by blood. Hebrews 9:18–22 says almost everything is cleansed with blood, and without the shedding of blood there is no forgiveness — the blood-splash of Leviticus 3:2 is a specific instance of the universal principle.
Leviticus 3:3
From the fellowship offering you are to bring a food offering to the Lord: the fat that covers the internal organs and all the fat that is connected to them. The fat — the rich, visceral covering of the internal organs — is the portion of the fellowship offering that belongs exclusively to God and is burned on the altar. The fat that covers and connects the internal organs is the body's reserve of richness and energy. Designating this fat as God's portion communicates that the richest, most vital part of what the animal contains belongs to the God who is the source of all richness and vitality. Deuteronomy 32:14 describes God feeding Israel with the fat of the land — the fat that Israel returns to God on the altar is from the same abundance God gave.