And Moses brought Aaron and his sons and washed them with water.
Leviticus 8:6

The priests underwent a group mikvah (baptism) in part symbolizing their transition from ordinary Israelite to priest, dying to one life and being reborn to another.

The High Priest's holiness allowed God to live among Israel, just as Yeshua's sinlessness allows Him to live in us. An unsanctified, unwashed priest is unfit to serve as priest.