And the priest that offereth any man's burnt offering,.... In which the flesh was wholly burnt, and nothing of it remained to requite the priest for his trouble, as in other offerings:even the priest shall have to himself the skin of the burnt offering, which he hath offered; in some cases the skin itself was burnt, and then he could have nothing, see Le 4:11 but in others the skin was reserved for the priest.
There seems to be an emphasis upon the phrase "to himself", and may signify, that though in other things other priests might partake with him, yet not in this; and so Maimonides observes, that the skin was not given to every priest, but to him that offered the sacrifice; and elsewhere he says, the skins of light holy things are the owner's, but the skins of the most holy things are the priest's.
And some have thought this law has some respect to the case of Adam, and is agreeable thereunto; who having offered sacrifice according to divine directions given him, had coats made for him and his wife of the skins of the slain beasts; and it was usual with the Heathen priests to have the skins of the sacrifices, and in which they slept in their temples and others also were desirous of the same, in order by dreams or otherwise to get knowledge of things future; See Gill on "Am 2:8".
In Misn. Challah, c. 4. sect. 9. In Misn. Zebachim, c. 12. sect.