Catching an object that was thrown to you (such as a ball) could represent: accepting an invitation to dialogue, play, or otherwise participate with the thrower; something in real life that you perceive as a game; receiving authority or something else that’s handed off to you (as in “now the ball is in your court”); communication, or receiving a message; completing a process; an event that you consider a success.
See also: Receiving; Ending; Succeeding; Throwing; Net; Hunting; Fishing; Caught, Being