used to stress that something is true, especially when it's surprising
As a matter of fact, I was just about to call you.
実は、ちょうどあなたに電話しようとしていました。
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.
彼はただの良い選手ではない;実際、彼はリーグで一番です。