The change, I think, that conversion gradually effects on your heart is this: you come, over some stretched-out time, to want to do the things that God wants you to do, because you want to be close to Him. So the point is not just to be forgiven, it is to be transformed. The religious languages have better words for this than English--teshuvah in Hebrew, and metanoia in Greek. A complete turning around.(Image: mine)
I doubt I will achieve a complete turning around here on Earth. I will always need this ritual of confession, because I will always keep screwing up. And God somehow will keep forgiving me, and pulling me closer to Him. He will, over time, make me sadder and sadder when I spit in His eye. He will make me love Him better. And that might mean, maybe, that I will sin a little bit less.
So Paul took his stand in the open space at the Areopagus and laid it out for them: "I'm here to introduce you to this God.... He doesn't play hide-and-seek with us. He's not remote; he's near. We live and move in him, can't get away from him!" ~Acts 17