The peace offering (Leviticus 3) speaks of the communion and fellowship of believers with God the Father through our Lord Jesus Christ. The only way you and I can come to God is through Jesus Christ. He is the Way!
No single offering can set forth the manifold wonders of the person of Christ and the many facets of His glory. Just as we need four Gospels in the New Testament to set forth His earthly life, so also we need the five offerings of Leviticus to set forth His person and work.
The peace offering does not speak of the peace that Christ made through His blood on the cross, as that has to do with sin and comes properly under the non-sweet savor offerings. Rather, the peace offering speaks more specifically of the peace to which Paul referred in Ephesians, the peace which brings all believers into communion with the Father by the Holy Spirit, through the Lord Jesus Christ. "But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ. For he is our peace, who hath made both one, and hath broken down the middle wall of partition between us; having abolished in his flesh the enmity, even the law of commandments contained in ordinances; for to make in himself of twain one new man, so making peace; and that he might reconcile both unto God in one body by the cross, having slain the enmity thereby" (Ephesians 2:13-16).
In the peace offering, the emphasis is not upon the peace that He made by the blood of the cross, but upon the peace He is because of the blood of the cross. He is the meeting place of all believers together and of each believer with God the Father. Christ is the only one who can break down the walls that separate individuals, families, religions, races, and nations. All are made one in Christ. Then they become a habitation of God in the Spirit and have access to the Father. You see, only believers can join together in partaking of the wonders, the beauties, and the glories of Christ. They can have communion with the Father and fellowship one with another as they share the things of Christ.
This is what the apostle John is saying. "That which we have seen and heard declare we unto you, that ye also may have fellowship with us: and truly our fellowship is with the Father, and with his Son Jesus Christ" (1 John 1:3). The peace offering brings us together. It is only as we meet around the person of Christ that we can be drawn together.
—From Edited Messages on Leviticus by J. Vernon McGee