The washing of the High Priest (& priests) was symbolic of the cleansing that we need to go through-for we cannot cleanse ourselves....
Take Aaron and his sons with him, and the garments, and the anointing oil, and a
bullock for the sin offering, and two rams, and a basket of unleavened bread; And gather thou all the congregation together unto the door of the tabernacle of
the congregation. And Moses brought Aaron and his sons, and washed them with water.
Leviticus 8:1,2,6
Not by works of righteousness which we have done, but according to his mercy he
saved us, by the washing of regeneration, and renewing of the Holy Ghost;
Titus 3:5