In "Word Focus" Danny McCain writes:

“Cleanse me from my sin.” The word used here (chatha) is the most common word for sin in the Old Testament. It basically means “to miss the mark” or “to come short of the goal.” Robert Girdlestone says, “If man was originally made in the image of God, it must have been implanted in him as a first principle that he should live as God lives. Every departure, therefore, from the law of right is a coming short of the purpose for which man was made, and a missing of the goal which ought to be reached” (Synonyms of the O.T.).

Source: Studies in the Psalms: Adult Teacher's Insights, page 46.