What does it mean to be a "man after God's own heart"?

"Blessed is he whose transgressions are forgiven, whose sins are covered. Blessed is the man whose sin the Lord does not count against him and in whose spirit is no deceit. " Psalm 32:1-2

So David said to Nathan, “I have sinned against the LORD.”

a. I have sinned against the LORD: David’s confession is a good example. He placed the blame squarely on his own shoulders. He did not minimize his offence. David realized that he especially sinned against God.

i. In the original Hebrew, David’s statement I have sinned against the LORD amounts to only two words: hata al-Yahweh. These two words, and the heart they reflect, show the fundamental difference between David and Saul. Confession doesn’t need to be long to be real and sincere. “The greatest griefs are not always the most verbal. Saul confessed his sin more largely, but less effectually.” (Trapp)

ii. “The words are very few, but that is a good sign of a thoroughly broken spirit. There is no excuse, no hiding, no concealment of the sin. There is no searching for a loophole, no pretext put forward, no human weakness pleaded. He acknowledged his guilt openly, candidly and without any denial of truth.” (Keil and Delitzsch)

iii. This was an exceptionally good response from a man of David’s standing in life. When confronted with sin, kings often say, “Off with their head.” David showed that God was working on his heart all along, and Nathan’s confrontation was just the last piece of that work.

https://enduringword.com/bible-commentary/2-samuel-12/