One of the consequences of sin is the disconnection between man and God and man and his fellow man. God, who dwells in His holiness, wants His people to also live in holiness. Sin takes that away. We no longer live a life based on His word, but on our own lusts.
This deep fear of separation from God is what is expressed in verses 11-15. The psalmist invites us to cry out loudly to God, "hide your face from my sin, blot out all my iniquities" (v.11). If God is believed to have been presenting His face to the people, now the psalmist asks for the opposite. The sins he committed made him feel unworthy of God's deep concern.
He didn't want that situation to last any longer so he asked God to blot out all his mistakes. The psalmist wanted God to purify his heart and from that came the joy of experiencing God's marvelous work of salvation. It is in response to God's work that the psalmist feels grateful and wants people to know God's forgiveness and mercy. And so, in the existence that God has restored for sins committed, the one thing that the psalmist longs for is to praise God and seek true repentance in daily life, because that is what God wants more than the burnt offerings that He commands.
Friends of the Bible, return to the arms of God, the Creator of the Universe. He waits lovingly for us. So approach Him with a surrendered heart and a full confession of our sins. God is present and expresses His mercy to those who ask Him for forgiveness. He will wash and purify our hearts.