This line is spoken by Miranda in Act 5, Scene 1, as she is experiencing the outside world for the first time. She is overwhelmed by the beauty and wonder of the world, and she sees it as a place full of potential and promise. The phrase "brave new world" is an allusion to the title of Thomas More's 1516 book "Utopia," which describes an ideal society. By using this phrase, Miranda is expressing her hope that the world she is about to enter will be a better place than the one she has known on the island.