Adam Clarke on Deuteronomy 18:3

Offer a sacrifice - זבחי הזבח zobechey hazzebach. The word זבח zebach is used to signify, not only an animal sacrificed to the Lord, but also one killed for common use. See Gen 46:1; Pro 17:1; Eze 39:17. And in this latter sense it probably should be understood here; and, consequently, the command in this verse relates to what the people were to allow the priests and Levites from the animals slain for common use. The parts to be given to the priests were,

1. The shoulder, probably cut off from the beast with the skin on; so Maimonides.

2. The two cheeks, which may include the whole head.

3. The maw - the whole of those intestines which are commonly used for food.