This play-within-a-play not only helps Hamlet to judge Claudius's guilt, but also acts as a spur for his own revenge: it shows him the murder that was done to his father and the murder that could be done to his uncle
The "play-within-a-play" in Hamlet is a play entitled The Murder of Gonzago, which Hamlet arranges to be performed at court by actors who have recently arrived at Elsinore Castle.
