Albert Barnes Commentary Leviticus 10:12-15

"And Moses spake unto Aaron, and unto Eleazar and unto Ithamar, his sons that were left, Take the meal-offering that remaineth of the offerings of Jehovah made by fire, and eat it without leaven beside the altar; for it is most holy; and ye shall eat it in a holy place, because it is thy portion, and thy sons` portion, of the offerings of Jehovah made by fire: for so I am commanded. And the wave-breast and the heave-thigh shall ye eat in a clean place, thou, and thy sons, and thy daughters with thee: for they are given as thy portion, and thy sons` portion, out of the sacrifices of the peace-offerings of the children of Israel. The heave-thigh and the wave-breast shall they bring with the offerings made by fire of the fat, to wave it for a wave-offering before Jehovah: and it shall be thine, and thy sons` with thee, as a portion for ever; as Jehovah hath commanded." — Leviticus 10:12-15 (ASV)

The argument is that as such meals were appointed in honor of Yahweh Himself, they ought to be conducted with due reverence and discretion (Leviticus 10:12).

Beside the altar - This refers to what is called “the holy place” in Leviticus 10:13 and Leviticus 10:17: it should, rather, be understood as a holy place, any part of the holy precinct, as distinguished from a merely “clean place” (Leviticus 10:14), either within or outside the court of the tabernacle.

Wave breast and heave shoulder - See the note on Leviticus 7:30.