We admitted to God, to ourselves, and to another human being the exact nature of our wrongs.
When we admit that we're sinners, like everyone else, we may assume that we're disqualified from being used by God to lead others. We may look up to those who seem so proud that God has kept them from sin and feel worthless in comparison.
In his confession of adultery and murder, David prays, "Do not banish me from your presence, and don't take your Holy Spirit from me. Restore to me the joy of your salvation, and make me willing to obey you. Then I will teach your ways to rebels, and they will return to you" (Psalm 51:11-13). David understood that admitting his wrongs would provide a bridge to other hurting souls.
This is quite different from the prayer he prayed as a young man, who had yet to realize that he was a sinner like the rest of us. Here's part of that prayer: "I hate the gatherings of those who do evil, and I refuse to join in with the wicked. . . . Don't let me suffer the fate of sinners. Don't condemn me along with murderers. Their hands are dirty with evil schemes, and they constantly take bribes. But I am not like that; I live with integrity. So redeem me and show me mercy" (Psalm 26:5, 9-11).
Admitting our sins doesn't disqualify us from being used of God. Recognizing the sin in our lives can only make us more useful to him. It allows us to glorify God for his grace and it removes any reasons we might have for exalting ourselves.
The more we've experienced God's forgiveness, the more we desire his presence and his joy.