What does the end of the play (specifically act 5, scene 2) convey to the audience?

As the end of Hamlet nears, numerous characters have already died, and it seems likely that the final resolution will include more deaths. As act V, Scene 2 opens, Hamlet reveals that his actions will have now caused two more deaths, those of Rosencrantz and Guildenstern. His commitment to duel Laertes confirms that another death is imminent.
During the duel, Claudius’s machinations to have Hamlet die either by poisoned sword or poisoned cup go awry. Simultaneously, Hamlet takes the poisoned sword and strikes Laertes, and Gertrude drinks the poisoned wine. Hamlet quickly gains control, killing Claudius twice over with the sword and the wine. Now Hamlet and Laertes will both die, but Horatio—Hamlet’s one true steadfast friend—must live.
Prior to this point, Hamlet himself had actually killed only Polonius, and that was only because he mistook him for Claudius. His actions led to several other deaths, however, including that of the innocent Ophelia. While he undertook his actions to identify and punish his father’s killer, and by extension to save his country, his hesitations and his poorly realized scheme created chaos, which is the antithesis of effective political rule. It is very likely that had he survived, Hamlet would not have been an effective king, and that his killing both King Claudius and the popular Laertes would have sparked a civil war in Denmark. Yet his destiny of punishing the guilty, including his promise to his father’s ghost, had to be fulfilled.
Along with Horatio’s survival, Fortinbras’s entrance and agreement to assume the throne reassure the audience that Denmark will be secure without further bloodshed. His comment on Hamlet’s royalty further shows that the prince’s memory will be respected.

The end of the play seems to signify the idea that anyone who contributed to the "something rotten" in Denmark has to be eliminated in order for the country to move on and prosper again.  Gertrude has to die because of her disloyalty to her first husband (shown by her hasty remarriage) as well as the fact that she has committed incest (biblically speaking) by marrying her brother-in-law.  Claudius has to die because he is a murderer (and has committed incest with his sister-in-law).  Laertes must die because he has behaved dishonorably in his dealings with Hamlet (by tipping his sword with poison during their duel).  Hamlet must die because he is responsible for the deaths of many relatively innocent individuals: Ophelia, Polonius, Rosencrantz, and Guildenstern.  In short, the heart of the Danish court has become a rotten, corrupted Eden, from which everyone who has committed sins must be cut out.  In the end, Fortinbras assumes power and it seems as though he will honor Hamlet's better qualities as well as restore order to the court and country.