Carl Friedrich Keil and Franz Delitzsch Old Testament Commentary

The Levites were then to close this transfer of themselves to the Lord with a sin-offering and burnt-offering, in which they laid their hands upon the sacrificial animals. By this imposition of hands they made the sacrificial animals their representatives, in which they presented their own bodies to the Lord as a living sacrifice well-pleasing to Him. The signification of the dedication of the Levites, as here enjoined, is still further explained in Num 8:13-19. The meaning of Num 8:13. is this: According to the command already given (in Num 8:6-12), thou shalt place the Levites before Aaron and his sons, and wave them as a wave-offering before the Lord, and so separate them from the midst of the children of Israel, that they may be Mine. They shall then come to serve the tabernacle. So shalt thou cleanse them and wave them. The same reason is assigned for this in Num 8:16, Num 8:17, as in Num 3:11-13 (כּל בּכור for כּל־בּכור, cf. Num 3:13); and in Num 8:18 and Num 8:19, what was commanded in Num 3:6-9 is described as having been carried out. On Num 8:19 see Num 1:53.