The Peace Offering or the Fellowship Offering
This was also an offering of a sweet savour to God. The blood, the fat and the kidneys of the offering were put upon the altar as "the food of the offering made by fire unto the Lord" (Leviticus 3:11). This was God's part.
Then the breast piece was given to Aaron and his sons and the right shoulder to the offering priest. This was man's part.
Thus God and man both fed on the same offering which speaks of communion and fellowship. This typifies the communion which the believer in Christ enjoys with God on the foundation of the work of Christ at the cross.
We are at peace with God through the work of the cross and can feed upon Christ in fellowship with the Father.
Luke's Gospel and Psalm 85 especially present this theme.
All the fat is the Lord’s. (Leviticus 3:16)
A person was not supposed to eat fat but was to offer it to the Lord
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