Leviticus 7

"This is the law of the sacrifice of peace offerings which he shall offer to the Lord:...the flesh of the sacrifice of his peace offering for thanksgiving shall be eaten the same day it is offered. He shall not leave any of it until morning.  But if the sacrifice of his offering is a vow or a voluntary offering, it shall be eaten the same day that he offers his sacrifice; but on the next day the remainder of it also may be eaten;  the remainder of the flesh of the sacrifice on the third day must be burned with fire."  vv.11, 15-17

Read chapter 7.
The peace offering is the last offerings mentioned after dealing with the sin offerings.  Perhaps to show the repentance and forgiveness must come first before true union with God.  The peace offering was like a shared meal with the priests, the offerer and God.  Certain parts were for the priests, the thigh and the breast and unleavened cake, for the offerer and his family, the meat and leavened bread, and for God, the fat.  There is a time limit set for when all of the offering must be eaten.  This could be due to no spoiling and causing uncleanness, also to not save for a banquet or other type of meal making the sacred sacrifice less meaningful and therefore not holy, set apart.  Whatever was not eat was to be burned and if anything was left it would not be accepted to the Lord.  I wonder how big of meals the offerings ended up being?  I couldn't imagine eating a Thanksgiving feast like we have today every day.  The cool thing about the peace offering can either be a have to or a vow or voluntary offering.  One thing I try to practice more is hospitality and offering meals for others more often, I just don't make them clean their plates if they don't want to.