“Washing” in the Bible represents purification - unsurprisingly! Washing dirt from the skin symbolizes using true ideas from the Lord to remove evil desires and false ideas from our minds. This is the reason that washing was such an integral part of ritual; cleaning the body to perform physical acts of worship - something with no actual spiritual value - is symbolic of repenting our evils and falsities as part of worshiping the Lord.
Exodus 24:16-18
16
The glory of Yahweh settled on Mount Sinai, and the cloud covered it six days. The seventh day he called to Moses out of the midst of the cloud.
17
The appearance of the glory of Yahweh was like devouring fire on the top of the mountain in the eyes of the children of Israel.
18
Moses entered into the midst of the cloud, and went up on the mountain; and Moses was on the mountain forty days and forty nights.
