Who is Miranda in The Tempest by Shakespeare?

In Shakespeare's The Tempest, Miranda is the daughter of Prospero, the former Duke of Milan living in exile on a remote island. Since Miranda has grown up in relative isolation (her chief companions are her father, Ariel, and Caliban), she is an innocent young girl who knows little of human society or the outside world. As such, when she meets the shipwrecked Ferdinand, she promptly falls passionately in love with him and eventually marries him. In Act 5, Scene 1, Miranda meets more of the shipwrecked characters and utters the famous quote, "O brave new world / That has such people in't!" (183-84), thus exemplifying her wonder and astonishment at her first brush with human society. The title of Aldous Huxley's dystopian novel Brave New World is a reference to this quote. 

All in all, Miranda is a girl who has grown up in isolation and is easily amazed by the new intrusions into her formerly secluded world. As such, many readers have seen her as a representation of a kind of pure human innocence. That said, it's important to note that Miranda's innocence relies on her relative ignorance when it comes to civilization and human relationships. Her father Prospero has seen the corruption and betrayal the world is capable of, and one can assume that, as Miranda matures and sees more of the world, she too will cease to idealize human society and come to view the world in a more realistic way.