Psalm 51 is a loaded Psalm. We're going to spend a few days here.
A bit of context going into this Psalm. David has just had Uriah murdered in order to hide his sin of having an affair with Uriah's wife Bathsheba and causing her to become pregnant. David was confronted by Nathan the prophet and now David is acknowledging his sin and asking God for forgiveness.
He begins the Psalm saying, "Be gracious to me, God, according to Your faithful love; according to Your abundant compassion, blot out my rebellion. Wash away my guilt and cleanse me from my sin. For I am conscious of my rebellion, and my sin is always before me." --Psalm 51:1-3
This is a man with a broken and contrite heart. He is crying out and pleading to God's gracious and loving nature. He is asking for forgiveness. Note that he acknowledges his sin when he says, "I am conscious of my rebellion." This is important: David knows that he has sinned and is confessing it to God.
I meet many people who don't want to confess their sin. To do so means that I am saying that I am living under someone else's authority and standard. It's like a child who won't admit that he broke curfew or took money from his dad's wallet. He or she defiantly and vehemently denies that they committed the act even though their crime is known by all.
With my own kids I would always say, "If you had only told me (confessed) before I found out from someone else or you denied it, I wouldn't be as angry. But you hid it from me." God feels the same way. Confess your sin to Him and ask for His forgiveness.
1 John 1:9 reads, "If we confess our sins, He [God] is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness." Sounds like the same God David was confessing to, doesn't it? He WILL forgive us, but it starts with acknowledgement and confession. Verse 10 says, "If we say, 'We don't have any sin,' we make Him a liar."
Let us acknowledge and confess our sin to God and ask for Him to wash away our guilt.