It looks like the same menu that pops up when you close the app or if the game crashes. I believe the center option continues where you left off, the right ends your current quest, and the left makes you start over.
You have to select the left option twice to restart completely though. I think it's meant to be used in case the app does crash, but you can use it to reset the quest if you are defeated. The best part is that it doesn't consume a magic stone.