What is the significance of Rosencrantz in Rosencrantz and Guildenstern are Dead by Tom Stoppard?
I'm not sure what you mean by significance, but the play is a coin flip, so to speak, of Shakespeare's Hamlet. Hamlet is a tragedy and if you flip the coin, you have comedy and in this case, Stoppard's play.
Rosencrantz and Guildenstern literally flip coins as the play opens. What Stoppard gives us is another view of the story from the point of view of two supporting characters who are clueless as to the bigger picture.
In the beginning, all they know is that they were sent for by Claudius. They spend much of the play waiting to find out what Claudius wants them to do and then waiting to do it. They pass the time by playing games, the coin flip is just one of the games they play.
These two may be very intelligent in the classroom but have no street smarts. They spend most of the play in the dark, so to speak, to the bigger picture. They are totally clueless.
The significance of this play is in the absurdity of it all.