Matthew Henry Commentary Leviticus 7:28-34

"And Jehovah spake unto Moses, saying, Speak unto the children of Israel, saying, He that offereth the sacrifice of his peace-offerings unto Jehovah shall bring his oblation unto Jehovah out of the sacrifice of his peace-offerings: his own hands shall bring the offerings of Jehovah made by fire; the fat with the breast shall he bring, that the breast may be waved for a wave-offering before Jehovah. And the priest shall burn the fat upon the altar; but the breast shall be Aaron`s and his sons`. And the right thigh shall ye give unto the priest for a heave-offering out of the sacrifices of your peace-offerings. He among the sons of Aaron that offereth the blood of the peace-offerings, and the fat, shall have the right thigh for a portion. For the wave-breast and the heave-thigh have I taken of the children of Israel out of the sacrifices of their peace-offerings, and have given them unto Aaron the priest and unto his sons as [their] portion for ever from the children of Israel." — Leviticus 7:28-34 (ASV)

The priest who offered was to have the breast and the right shoulder. When the sacrifice was killed, the offerer himself was to present God's part of it, to signify his cheerfully giving it up to God. He was to lift it up with his own hands, as a sign of his regard for God as the God of heaven, and then to wave it back and forth, as a sign of his regard for God as the Lord of the whole earth.

Be persuaded and encouraged to feed and feast upon Christ, our Peace-offering. This blessed Peace-offering is not for the priests only, for saints of the highest rank and greatest eminence, but also for the common people. Beware of delay. Many think to repent and return to God when they are dying and dropping into hell, but they should eat the peace-offering, and eat it now.

Do not wait until the day of the Lord's patience runs out, for eating the third day will not be accepted, nor will catching at Christ when you are gone to hell! (Leviticus 7:35–38)