the ball is in someone's court
the ball is in (one's) court
One has the responsibility for further action, especially after someone else previously held responsibility. The phrase originated in tennis. Well, they invited you, so the ball is in your court now. Do you want to go out with them or not?
the ball is in someone's courtit is that particular person's turn to act next.
This expression is a metaphor from tennis or a similar ball game where different players use particular areas of a marked court.