What does Psalm 51:7 mean?

Again, David pleads for cleansing. He asks the Lord to purge him with hyssop to make him clean and to wash him to make him whiter than snow. To purge meant to purify by removing a stain. Hyssop was a plant that the priests used in ceremonial cleansings. They dipped a bunch of hyssop in the blood of a sacrificial animal and then sprinkled the blood on the person who required cleansing. Leviticus 14:4–7 refers to the use of blood-dipped hyssop in sprinkling seven times the person who is to be cleansed of leprosy.

David recognized that he would be whiter than snow if the Lord washed away his sin. In Isaiah 1:18 the Lord invited the sinful people of Judah to come to Him and reason with Him, promising, "Though your sins be as scarlet, they shall be as white as snow; though they are red like crimson, they shall become like wool." When Jesus washed His disciples' feet in the upper room, He told unwilling Peter he would have no share with Him unless He washed them (John 13:8).