Today, we typically use the term peace offering to mean an attempt to make amends through a gift or action, usually after an interpersonal transgression. We see it as an attempt to make peace. But the biblical usage is quite different. The peace offering, found in Leviticus 7, pictures an individual and the priest in fellowship with God because God has already bestowed His favor in some way. It is often called a thanksgiving offering because it is made in response to what God does for the individual. The true peace offering shows that there is peace instead of trying to create peace.
Because of the many possible meanings of the Hebrew word for the peace offering, commentators also call it the thanksgiving offering, fellowship offering, or communion sacrifice, and hold onto that last one - the communion sacrifice.
The peace offering pictures a shared meal with God where there is harmony and satisfaction because everyone is at peace with each other - and that includes God Himself. It is an occasion with feelings of security and well-being. The peace offering celebrates that the relationship between God and the individual is on good terms, which should be a cause for extreme gratitude. The Passover is a prime example of this, where God made an exemption and accepted Israel when He should have destroyed her if He were intent on justice. Granted, the harmony at that point in the relationship was not ideal, and that may be why God told them to eat soberly or with serious consideration. But considering what Israel deserved, God was overwhelmingly peaceful in His acceptance and overlooking.
So, the peace offering was a meal, like the Passover. Both were to be eaten the same day the sacrifice was performed. For both sacrifices, none was to remain until morning, but what remained had to be burned (Exodus 12:10; Leviticus 7:15). And like the Passover, the peace offering was not limited to being eaten by the priests. It also did not have to be eaten at the tabernacle, nor were any parts of the animal excluded, as with the sin offering. The most significant difference between the peace offering and the Passover is that the peace offering included both leavened and unleavened bread, while the Passover only allows unleavened bread. So, Passover is not a typical peace offering - it is a step above, and of course, it is far more important because it is only performed once a year.
The peace offering is an example of a blood sacrifice that is for purposes other than the payment for sin. It shows a life given, and the result of that sacrifice is a shared meal of fellowship. In this meal, God is satisfied because man is in fellowship with Him, and man is satisfied because God graciously accepts him and provides for his well-being.