What does Hamlet mean when he says, "The play's the thing / Wherein I'll catch the conscience of the King"?

Rince Hamlet has been told by the ghost of his father, King Hamlet, that Prince Hamlet's uncle, King Claudius, murdered his own brother, King Hamlet. Claudius then married the dead King Hamlet's wife and Prince Hamlet's mother, Queen Gertrude. Since Hamlet does not know if the ghost is truly his father and telling the truth, he devises a plan that he believes will prove if what the ghost has said is true.

Actors have come to perform at Elsinore Castle for King Claudius and Queen Gertrude. Hamlet asks them to use his altered version of the play, in order to "catch the conscience of the King." The alteration tells the story of a Queen whose husband is murdered by poison. The poisoner then woos the Queen with gifts. Though she rejects him for awhile, in the end she accepts his love. Hamlet plans to watch Claudius' reaction to the altered portion of the play, and discern from that response if Claudius is guilty. His fear of King Claudius' power, and his desire to shame his mother, Queen Gertrude, is the reason for Hamlet's indirect method of accusing the King. If Hamlet's plan does