John Gill Commentary Numbers 8:21

"And the Levites purified themselves from sin, and they washed their clothes: and Aaron offered them for a wave-offering before Jehovah; and Aaron made atonement for them to cleanse them." — Numbers 8:21 (ASV)

And the Levites were purified From sin, by the sprinkling of the sin water, or water of purification on them, (Numbers 8:7) ;

and they washed their clothes ; that they might have no defilement about them, neither in their bodies, nor in their garments:

and Aaron offered them [as] an offering before the Lord ; a wave offering, as in (Numbers 8:11) ;

and Aaron made an atonement for them to cleanse them ; by offering the sacrifices for them, (Numbers 8:12) .