The priests the Levites, the whole tribe of Levi; i.e. the whole tribe of Levi, including both the priests and the general body of the Levites. They shall eat the offerings of the Lord made by fire. "The offerings of the Lord made by fire" (literally, the fires or firings of Jehovah), here referred to, were the meal offering, the sin offering, and the trespass effusing (cf. Numbers 18:9). And his inheritance; i.e. of Jehovah, what was appropriated to him, and from him to the tribe of Levi, such as tithes, firstlings, and firstfruits.
As he hath said unto them (cf. Numbers 18:20). The shoulder, and the two cheeks, and the maw; i.e. the front leg, the two jaw-bones, and the rough stomach of ruminants, in which the digestion is completed. These were regarded as the choice parts of the animal, and were to be given to the priests in addition to the wave breast and heave leg of the peace offerings (Le 7:32, etc.; Numbers 18:11), which belonged to the firings of Jehovah, mentioned in Deuteronomy 18:1. To these the priest had a rightful claim; they were his due ( מִשְׁפַט, mishpat, right). "This right was probably accorded to the priests as a compensation for the falling off which would take place in their incomes in consequence of the repeal of the law that every animal was to be slaughtered at the sanctuary as a sacrifice (Leviticus 17:1-16; vide Deuteronomy 12:15. sqq.)"(Keil). According to Josephus ('Antiq,' 4.4, 4), Philo, the Talmud, etc; this injunction relates to the slaying of animals at home for private use, and not such as were killed for sacrifice. But the use here of the sacrificial phraseology, who offer a sacrifice ( זֹבְחֵי הַזֶּבַח, who slay victims for sacrifice—a phrase nowhere found except in connection with sacrificial rites) is adverse to this; and besides, how could such an enactment be carried out? How could people, residing at a distance, convey to the priests the portions due to them every time they slaughtered an animal for domestic use? At the same time, the sacrifices here referred to do not seem to be included in the offerings by fire above mentioned; and these gifts to the priest seem to have been something over and above his ordinary dues. There is probability, therefore, in the suggestion that "the reference is to the slaughtering of oxen, sheep, or goats, which were not intended for shelamim in the more limited sense, i.e. for one of the three species of peace offerings (Le Deuteronomy 7:15, Deuteronomy 7:16), but for festal meals in the broader sense, which were held in connection with the sacrificial meals prepared from the shelamim" (Keil).