Let's start with a recap: The play ends with Guil attempting to stab the Player, who fakes his death only to stand up and reveal that the knife Guil used was a prop. The stage goes dark, leaving Guil and Ros side by side in the dark (not too different from the beginning). Ros disappears, and then so does Guil. Then the lights go up on the closing scene from Shakespeare's Hamlet. The ambassador announces that Rosencrantz and Guildenstern are dead, and Horatio makes his final speech.
There is a ton going on here. We'll try to discuss a few of the more complicated aspects, but you might have other ideas to add, too. First, Guil and the Player are arguing about death. Guil is accusing the Player of not being able to capture death in his plays. As he says, "You die a thousand casual deaths – with none of that intensity which squeezes out life … and no blood runs cold anywhere" (3.123). Angry and emotional (knowing that he is on the way to his own death), Guil attempts to teach the Player a lesson by stabbing him: to show him the difference between his acted deaths and real death. Guil wants the Player to realize the kind death he and Ros face. In his words, "death is not… It's the absence of presence, nothing more … the endless time of never coming back … a gap you can't see, and when the wind blows through it, it makes no sound …" (3.124). He wants to bring home the reality of death to the Player, but, needless to say, if he kills him, the Player won't learn the lesson (since he'll be dead). On the other hand, maybe he will (since he'll be dead).
Now, the Player, knowing that he has been stabbed with a false knife, pretends to die in front of Guil. Even in their actions, the two are still arguing. By convincingly faking the death, the Player is showing Guil that he (Guil, that is) cannot tell the difference between a real death and a fake one. For all Guil's talk, he won't actually know what death is like until he's dead.
When the stage goes dark, Ros, the more oblivious of the two, begins to question their situation. He protests that "We've done nothing wrong" (3.125). He briefly desires that there be some justification, some reasonable explanation, for their deaths. Instead, he gives up and… disappears. Guil reflects back to the mysterious messenger that summoned the two of them some time before the beginning of the play. He thinks that they must have been offered a way out at some point, that there was a place where they could have avoided their fate. His pondering on chance and fate recalls the beginning of the play in which the laws of probability are suspended in the coin flip. It is unclear if, in the world these two inhabit (the world of the play), the laws of chance and fate are operating normally or not. Needless to say, the same questions can be asked about our own world.
The ending pulls together a couple of themes that run throughout the play: the impossibility of capturing death on the stage, and the tension between viewing the world as ruled either by chance or by fate. It is worth noting that at least one of these themes – the impossibility of capturing death on the stage – relates very closely to a problem that Sir Tom Stoppard faces as he is writing the end of his play. He has reached the part in the action where Rosencrantz and Guildenstern die, but the whole discussion that precedes it is about the inability of a play to portray death. It's significant that Rosencrantz and Guildenstern do not die on stage, but simply disappear, as Guil himself predicts earlier on in the play: "You can't act death. The fact of it is nothing to do with seeing it happen—it's not gasps and blood and falling about—that isn't what makes it death. It's just a man failing to reappear, that's all—now you see him, now you don't" (2.84).
Unlike Hamlet, with its abundance of melodramatic deaths, Stoppard's play does not claim that it can actually portray death on the stage. We see this when Horatio makes his speech and announces that he will "truly deliver" the events that took place. As he speaks, the lights are already going dim and the music is starting to signify the end of the play. The play just ends without respecting Horatio's speech; it cuts him off. As a result, the ability of the playwright to "truly" portray a series of events, death foremost among them, is called into question.