In this verse, David acknowledges that he is a sinner by nature as well as by practice. In the same way that all human beings are born with a sinful nature, David was no exception. It is true that all human beings commit sins by nature because they are sinners by nature, just as an apple tree bears apples by nature because it is an apple tree. 
David, like all young boys and girls, was not taught to do wrong. Both his mother and grandmother committed sins, as did his father and forefathers. As a result, he was conceived by two sinful parents from Adam's fallen race. In fact, the sinful, fallen nature inherited by all of humanity through Adam was the cause of the sinful actions.
All of us are the children of fallen parents. All of us are sinners with a sinful nature. Each of us was born into iniquity, and each was conceived by fallen parents. However, praise God that through the sacrifice of Christ on the cross, we have been redeemed from our sins. The amazing plan of redemption, which David enjoyed so long ago, is still available to all who will trust in Christ today.

Dear Heavenly Father, we thank You for Your plan of redemption that gives all men and women the opportunity to turn to You for forgiveness of sin and eternal life. I thank You for being faithful and just, forgiving me, and cleansing me from all unrighteousness when I confess my sin to You. For my sinful actions, I pray that I will not attempt to justify them or blame others. And I pray that I live my life to honor You. 
In Jesus's name I pray. Amen.