the ball is in your/somebody's court: it is your/somebody's responsibility to take action next (球已经丢给你了)下一步就看你的了

They've offered me the job, so the ball's in my court now. 他们已答应把那份工作给我,下一步就看我怎么办了.

I've given them a list of the changes that I think are necessary, so the ball's in their court now.

Be on the ball: be aware of what is happening and be able to react or deal with it quickly 警觉,能随机应变

For the assiatant manager's job we need someone who's really on the ball. 经理助理一职我们需要一个精明干练的人来担任.