Being just the two of them, with no third person present; often used between close friends or couples.
今日は二人きりで食事に行かない？
Shall we go out to eat just the two of us today?
秘密の話があるから、二人きりで会おうと言った。
I said let's meet just the two of us because I have something private to tell you.
親になると、子どもと二人きりの時間も大切になる。
When you become a parent, the time spent alone with your child also becomes important.