“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
And the glory of the LORD abode upon mount Sinai, and the cloud covered it six days: and the seventh day he called unto Moses out of the midst of the cloud.
17
And the sight of the glory of the LORD was like devouring fire on the top of the mount in the eyes of the children of Israel.
18
And Moses went into the midst of the cloud, and gat him up into the mount: and Moses was in the mount forty days and forty nights.
