To feel satisfied or to have one's mind put at ease; to be content after something has been resolved or completed.
全部説明してやっと彼は気が済んだようだ。
After explaining everything, he finally seemed satisfied.
お土産を買ってきたら、母の機嫌も良くなって気が済んだ。
When I bought a souvenir, my mother's mood improved and I felt relieved.
何度も確認してやっと気が済んだ。
I checked it many times and finally felt satisfied.