What does Psalm 51:2 mean?

In this verse David continues asking God to forgive his sin. He pleads with God to wash him completely from his iniquity and to cleanse him from his sin. His sin had made him feel as defiled as someone who had touched something unclean, or as helpless as someone touched by a disease (Leviticus 11:32; 13:1–3). He longed to have a new start in life, like a person who washed and put on new, clean clothes (Genesis 45:21–22; Exodus 19:10, 14).

In his letter to the Ephesians the apostle Paul referred to the believer's former life of sin as "the old self" and the redeemed life as "the new self." Like changing their clothes, the Ephesian Christians were exhorted to "put off your old self, which belongs to your former manner of life and is corrupt through deceitful desires…and to put on the new self, created after the likeness of God in true righteousness and holiness" (Ephesians 4:22, 24).