A suffix attached after a number to indicate the ordinal count (e.g., 'the nth time'); expresses how many times something has occurred.
今日は三回目の授業です。
Today is the third lesson.
そのイベントは今年で十回目を迎える。
This year that event will reach its tenth edition.
もう二回目だから、少し気楽です。
It's the second time already, so I'm a bit more relaxed.