From Chabad.org: We now read about the induction of the priests and the inauguration of the Tabernacle. In the presence of all the Jews, Moshe dressed Aaron and his sons in the priestly vestments and anointed them, along with the Tabernacle and its vessels, with the holy anointing oil.
I find it fascinating that the Jews were invited to see not only the inauguration of the Tabernacle, but how the priests got ready to serve. They bathed (modestly, no doubt), dressed with the proper garb, received the oils (on their heads). I think it continues the important theme that being ready and performing Mitzvot (good deeds) is so much more than just executing them. Preparing for them, and being in a position to perform them, is of equal importance. That’s the beauty of living in a Jewish community. It allows for more opportunities to help others, contribute to the community as a whole receive and host new members, and that’s besides the advantage of feeling like we belong. But it all start with preparing and putting ourselves in a position to succeed and perform, which is what the Cohanim were doing just prior to the inauguration.