A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
lev 9:1THE PRIESTS' ENTRY INTO OFFICE. (Lev. 9:1-24)
Moses called . . . Take thee a young calf for a sin offering--The directions in these sacred things were still given by Moses, the circumstances being extraordinary. But he was only the medium of communicating the divine will to the newly made priests. The first of their official acts was the sacrifice of another sin offering to atone for the defects of the inauguration services; and yet that sacrifice did not consist of a bullock--the sacrifice appointed for some particular transgression, but of a calf, perhaps not without a significant reference to Aaron's sin in the golden calf [Exo 32:22-24]. Then followed a burnt offering, expressive of their voluntary and entire self-devotement to the divine service. The newly consecrated priests having done this on their own account, they were called to offer a sin offering and burnt offering for the people, ending the ceremonial by a peace offering, which was a sacred feast. This injunction, "to make atonement for himself and for the people" (Septuagint, "for thy family"), at the commencement of his sacred functions, furnishes a striking evidence of the divine origin of the Jewish system of worship. In all false or corrupt forms of religion, the studied policy has been to inspire the people with an idea of the sanctity of the priesthood as in point of purity and favor with the Divinity far above the level of other men. But among the Hebrews the priests were required to offer for the expiation of their own sins as well as the humblest of the people. This imperfection of Aaron's priesthood, however, does not extend to the gospel dispensation: for our great High Priest, who has entered for us into "the true tabernacle," "knew no sin" (Heb 10:10-11).
lev 9:8Aaron . . . went unto the altar, and slew the calf of the sin offering--Whether it had been enjoined the first time, or was unavoidable from the divisions of the priestly labor not being as yet completely arranged, Aaron, assisted by his sons, appears to have slain the victims with his own hands, as well as gone through all the prescribed ritual at the altar.
lev 9:17meat offering . . . wave offering--It is observable that there is no notice taken of these in the offerings the priests made for themselves. They could not bear their own sins: and therefore, instead of eating any part of their own sin offering, as they were at liberty to do in the case of the people's offering, they had to carry the whole carcasses "without the camp and burn them with fire" [Exo 29:14; Lev 4:12].
lev 9:22Aaron lifted up his hand . . . and blessed them--The pronouncing of a benediction on the people assembled in the court was a necessary part of the high priest's duty, and the formula in which it was to be given is described (Num 6:23-27).
came down from offering--The altar was elevated above the level of the floor, and the ascent was by a gentle slope (Exo 20:26).
lev 9:23Moses and Aaron went into the tabernacle--Moses, according to the divine instructions he had received, accompanied Aaron and his sons to initiate them into their sacred duties. Their previous occupations had detained them at the altar, and they now entered in company into the sacred edifice to bear the blood of the offerings within the sanctuary.
the glory of the Lord appeared unto all the people--perhaps in a resplendent effulgence above the tabernacle as a fresh token of the divine acceptance of that newly established seat of His worship.
lev 9:24there came a fire out from . . . the Lord--A flame emanating from that resplendent light that filled the holy place flashed upon the brazen altar and kindled the sacrifices. This miraculous fire--for the descent of which the people had probably been prepared, and which the priests were enjoined never to let go out (Lev 6:13) --was a sign, not only of the acceptance of the offerings and of the establishment of Aaron's authority, but of God's actual residence in that chosen dwelling-place. The moment the solemn though welcome spectacle was seen, a simultaneous shout of joy and gratitude burst from the assembled congregation, and in the attitude of profoundest reverence they worshipped "a present Deity."