David reflects on the darkest moment of his life and how far he has fallen from God, but recognizes that even as great as his sin is God's mercy is greater.
New beginnings require a revelation of sin (acknowledge its power and the damage it can do). David takes ownership of his sins (doesn't blame circumstances or others) and realizes the problem is in his own heart. We always sin against God before we sin against others. He understands that sin has been a part of his life ever since birth. He knows that God is righteous and has the authority to judge Him for his sins.
We need a revelation of God's character. David knows the one he is praying to is a God of unfailing love and mercy. God loves us and wants to forgive us and he has paid for our sins in the person of Jesus. We need God to wash our deceitful heart and make it one that reflects God's character. Once God touches our lives, we should praise God and seek to reach people and to further God's kingdom.