Responsibility is yours. The ball is in your court means that the responsibility has passed to you, that the decision in a given situation is up to you, and that it is up to you to make the next move. When the ball is in your court, nothing else can happen in a given situation until you take action or make a decision. The idiom the ball is in your court is derived from the sport of tennis. When the ball bounces in your court during a game of tennis, you must take action and hit it to keep the game going. The expression the ball is in your court, expressed in a figurative sense, came into use in the 1960s.

Source: Grammarist