So, one day, he looks out from his roof and sees a gorgeous girlie in the bath (accidentally, of course), so he exercises his "right" as King and sleeps with her, knowing full well her husband was one of his best soldiers, Uriah the Hittite. Anyway, young Bathsheba (for 'twas her name) gets preggers and David gets a bit worried. As you would.
He calls for your man Uriah and gives him a leave of absence, the plan being that he'll toddle off home to "see" his missus, then the baby can be named Uriah Junior, no-one's any the wiser, and everybody's happy. Triffic! Unfortunately Uriah had other plans - he was such a loyal guy that he slept outside David's palace, so he could be at his King's command at all times. David, a bit peeved at this, decides to send his man to the front line, where men were dying every day, and withdraw all his soldiers except Uriah at a critical moment, so the Hittite would be out of the way. Permanently. This happens according to plan, David marries Bathsheba and Davey boy gets away with it. Or not.
You see, even though we think no-one has seen our sin, God has. David gets visited by Nathan the prophet and told that, because of his sin, his house would suffer some serious strife in years to come. But, crucially, he is also told "The LORD has taken away your sin. You are not going to die." David is forgiven and he makes sure that he doesn't repeat his sin.
Even though we commit the "worst" sins, and try to get away with it, God sees them and still forgives them. He loves us that much.
Read more in 2 Samuel 11-12 and Psalm 51