In the peace offering, Christ is the priest, offeror, and offering. Since all parties share the peace offering as a meal, it exemplifies a peaceful communion.
The meal offering represents the intense self-sacrifice required in service to man. Our service to man must be done for God's sake rather than man's appreciation.
The sacrifices were neither insignificant nor barbaric, but a teaching tool for us. In the burnt offering, we see Christ in His work for the already redeemed.
The meal offering represents the second Great Commandment, love toward fellow man. Our service to others requires much grinding self-sacrifice and surrender.
The burnt offering is completely consumed on the altar. This type of offering teaches us about Christ's total dedication to God—and how we should emulate it.
[Editors Note: Audio quality improves at the 4 minute mark.]
The peace offering teaches many things, but one of its main symbols is fellowship. Our communion with the Father and the Son obligates us to pursue peace.