Ender finds this door as he plays his private game in Chapter 7. As he enters, he finds himself in a tower that has no visible means of escape. Interestingly, at this point the game is finished as Ender receives a message to go and report to his commander, but Ender leaves imagining that "The End of the World" represents the end of all the games he is forced to play, where he can enjoy real life and live normally.
Perhaps it's called the end of the world because it's the end of the games, because I can go to one of the villages and become one of the little boys working and playing there, with nothing to kill and nothing to kill me, just living normally.
Note that in Chapter 9 Major Imbu says that this phrase "has a private meaning for Ender," and he certainly is right, as Ender associates this tower room with a hoped-for future where he will be able to live a life free from the machinations of others.
Of course, as the novel develops Ender understands that "The End of the World" is actually the buggers communicating with him and preparing him for the resurrection of their species after Ender has committed genocide. "The End of the World" therefore functions as a multi-layered symbol, standing for a potentially happier future for Ender where he can be free, but also refering to the genocide of the aliens and Ender's role in their rebirth.