Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
The actual lighting of the lamps (compare the marginal references) was to be done to set forth symbolically the special presence which God had now Num 7:89 actually established among His people.
The Levites could only undertake their duties Num. 3; 4 after the formal exchange of the Levites for the first-born Num 3:44-51.
The distinction between the "consecration" of the priests Lev. 8 and the less solemn "purification" Num 8:21 of the Levites is marked. These rites of purification are similar to those incumbent on the priests of Egypt.
Water of purifying - literally, "sin water:" i. e. water to cleanse from sin; no doubt taken from the laver of the sanctuary, which was used by the priests for purification before they went into the tabernacle to minister (compare Num 5:17; Exo 30:18 ff).
The "sprinkling" of so large a body of men could have been only general, but tokens of individual purification are specified (compare also Lev 14:8).
The two bullocks were "to make an atonement for the Levites," and therefore are presented in their name. These offerings are similar to those prescribed in Lev 8:14 ff at the consecration of the priests, except that the burnt-offering was on that occasion a ram. The larger victim corresponds to the larger number of the Levites.
The children of Israel - i. e. through the heads of their tribes, who Num 7:2 no doubt acted for their tribesmen. This act, the distinguishing feature of the ceremony, represented the transfer to the Levites of the sacred duties originally incumbent on the whole people.
Offer ... offering - Compare the margin Aaron pointed to the Levites, and then waved his hands, indicating (compare Lev 7:30 note) that the offering was dedicated to God, and, again, by grant from Him, withdrawn for the use of the priests.
Make an atonement for the children of Israel - i. e. by performing those services which were due from the children of Israel; the omission of which by the children of Israel would, but for the interposition of the Levites, have called down "wrath" from God, or Num 1:53 "plague." The institution of the Levites was an extension of that mediatorial system which the people themselves, terrified at the direct manifestations to them of the divine presence, desired; see Deu 5:25. Further, it is suggested to us here as an act of mercy on the part of God; yet even the priests and Levites themselves were not always sufficiently heedful and reverent. Compare Num 17:10; Lev 10:1 ff; Sa2 6:6 following.
Were purified - Rather, purified themselves; as directed in Num 8:7.
Twenty and five years old and upward - The permanent limit as distinguished from the temporary Num 4:3, Num 4:23, Num 4:30, though David found it necessary to extend the period of the Levites' service by causing it to commence at 20 years of age Ch1 23:24-28. This rule continued in force from the time of David downward (compare on Ch2 31:17; Ezr 3:8).