used to stress that something is true, especially when it's surprising
As a matter of fact, I was just about to call you.
사실, 방금 당신에게 전화하려고 했어요.
used to add more information or correct something
He's not just a good player; as a matter of fact, he's the best in the league.
그는 단지 좋은 선수가 아니다; 사실, 그는 리그에서 최고입니다.