What is Hamlet saying in Act 2, scene 2, lines 500-549?
Hamlet is comparing himself and his lack of response to the Ghost's directive to seek revenge with the impassioned speech just given by one of the actors. The Player has no personal reason to be so passionate ("What's Hecuba to him, or he to Hecuba/That he should weep for her?"), yet his performance has moved his audience to tears. Hamlet, on the other hand, does have reason to feel great loss because of the murder of his father, yet he has done nothing so he criticizes himself: "Am I a coward?" The actor as a character foil for Hamlet leads him to see more clearly his own flaws at this point in the play.
Then Hamlet thinks of a plan by which he can test Claudius' guilt because he wants to be certain before he does act. He describes a scenario in which a re-enactment of the murder performed in front of the murderer is likely to provoke a confession from the guilty party. Hamlet will have the actors perform such a scene, and he will closely watch Claudius to see if the king reacts. Stirred to action by the actor's speech, Hamlet determines "The play's the thing" to find out if Claudius is guilty.