Welcome to English in a Minute. American English has many idioms that come from sports. This one comes from tennis. The ball is in your court.
Jonathan, how did your date with my friend Caroline go? It went great, but when I texted her, she didn't respond. So I guess it's over. No, you can't give up like that.
Text her again. The ball's in her court. And tennis, you can only hit the ball when it is on your side of the court. When the ball is in your court, you can take action.