The second time something happens or is done; indicates the occurrence or opportunity for the second instance.
彼に会うのはこれで二度目だが、前よりずっと話しやすくなった。
This is the second time I've met him, but he's much easier to talk to than before.
同じミスを二度目にしないように気をつけてください。
Be careful not to make the same mistake a second time.
２度目の試験では問題の出題形式が変わっていた。
On the second exam, the format of the questions had changed.