What does Psalm 51:9 mean?

In this verse David asks the Lord to do two things. First, he asks God to hide His face from David's sins, and second to blot out David's transgressions. David implores the Lord to turn away from David's sins and no longer look at them.

On the cross Jesus bore our sins in His body (1 Peter 2:24). Jesus also sensed that the Father turned away from Him. Quoting from another psalm of David's, Psalm 22, Jesus cried out, "My God, my God, why have you forsaken me?" (Matthew 27:46). Of course, the answer to Jesus' question is this: God is "of purer eyes than to see evil and cannot look at wrong" (Habakkuk 1:13). He turned away His eyesight from Jesus, our sin-bearer, so He would not have to turn away from us in eternity. David longed for the Lord to turn away from his sins so he would be acceptable in His sight. He also wanted the Lord to erase his iniquities from the record, just as a judge might erase a criminal's crimes from the record books.