What is the "play-within-a-play" in Hamlet?

The "play-within-a-play" is this acting out of "The Murder
of Gonzago," or, has Hamlet has renamed it, "The Mousetrap," inside the play by
Shakespeare, Hamlet.

In Act 2, Scene
2, Hamlet has just finished grilling Rosencrantz and Guildenstern about their motives.
They dissuade him from his anger by pointing out a band of traveling actors who has just
made their way onto the grounds of Elsinore.

In a primary
example of Hamlet's intellectually quick mind, the prince immediately forms an idea.
There is a traditional play that many actors know called "The Murder of Gonzago." This
play depicts the murder of a king.

readability="5">

The play's the
thing

Wherein I'll catch the conscience of the King
(2.2.633-34).

Hamlet pulls
one of the actors aside and asks him if he can "modify" the script a little. He asks the
players to memorize sixteen lines that he himself will compose and that the players are
to incorporate into their act. These lines will reflect the details of Claudius and
Gertrude's treachery:

Hamlet eagerly anticipates
Claudius' reaction to the scene. He believes that if Claudius reacts negatively (as
Hamlet is quite sure he will), that proof of the Ghost's assertions will be validated.
Remember, at this point, Hamlet is still wary of trusting the Ghost. It is quite
possible that the Ghost may be an evil spirit coming to him in the guise of his beloved
father. However, if Hamlet gets the proof he needs, via Claudius' reaction, he will know
the Ghost can be trusted.