Psalm 51 is a compelling Psalm about broken fellowship with God and the desire to have that fellowship restored. In context, the Psalm was written by David after his sin with Bathsheba. We know that the sins of adultery and murder weighed heavily on David's heart. Although his sin affected others around him, it was ultimately the Lord that he sinned against.
David recognizes all of this and through Psalm 51, he implores God not to take away the presence of His Holy Spirit. In being restored, he also believes he can be used as someone to teach transgressors the ways of the Lord. Through reading this passage, we can learn much about our process of redemption...whether we are brand new to accepting Christ OR if we have backslidden in some aspect of our faith.