Bible Notes Online - Leviticus 3 - ESV
Commentary

v1: The Fellowship, or Peace, Offering, bringing propitiation by blood.

v3-4: See also v9-10,14-15; the inner parts of the animal was offered, the secret part for God. Christ's devotion was totally for the Father; and ours should be also. This implies a regular meeting with Christ, and a deep and growing devotion to Him.

The kidneys and loins speak of compassion and fruitfulness, respectively. Such qualities are the out-working of a life of devotion to God.

See also 7.11-21, for more instructions about this offering, including which parts were to be eaten by the priests. Thus, God's people are blessed by our devotion to Christ.

v17: The fat and blood cannot be eaten. See also 7.22-27.

It is said that the peace offering, was the offering of completion, as it always followed the other offerings. Also the most joyful. (Afred Edersheim, The Temple, its Minstry and Service)