Complete Commentary on the Whole Bible, by Matthew Henry, at sacred-texts.com
(Lev 3:1-5) The peace-offering of the herd.
(Lev 3:6-17) The peace-offering of the flock.
The peace-offerings had regard to God as the giver of all good things. These were divided between the altar, the priest, and the owner. They were called peace-offering, because in them God and his people did, as it were, feast together, in token of friendship. The peace-offerings were offered by way of supplication. If a man were in pursuit of any mercy, he would add a peace-offering to his prayer for it. Christ is our Peace, our Peace-offering; for through him alone it is that we can obtain an answer of peace to our prayers. Or, the peace-offering was offered by way of thanksgiving for some mercy received. We must offer to God the sacrifice of praise continually, by Christ our Peace; and then this shall please the Lord better than an ox or bullock.
Here is a law that they should eat neither fat nor blood. As for the fat, it means the fat of the inwards, the suet. The blood was forbidden for the same reason; because it was God's part of every sacrifice. God would not permit the blood that made atonement to be used as a common thing, Heb 10:29; nor will he allow us, though we have the comfort of the atonement made, to claim for ourselves any share in the honour of making it. This taught the Jews to observe distinction between common and sacred things; it kept them separate from idolaters. It would impress them more deeply with the belief of some important mystery in the shedding of the blood and the burning the fat of their solemn sacrifices. Christ, as the Prince of peace, "made peace with the blood of his cross." Through him the believer is reconciled to God; and having the peace of God in his heart, he is disposed to follow peace with all men. May the Lord multiply grace, mercy, and peace, to all who desire to bear the Christian character.