The titleBrave New Worldderives from Miranda's speech in William Shakespeare's The Tempest, Act V, Scene I:
O wonder!
How many goodly creatures are there here!
How beauteous mankind is! O brave new world,
That has such people in't.
— William Shakespeare, The Tempest, Act V, Scene I, ll. 203–206
Shakespeare's use of the phrase is intended ironically because the speaker's innocence means she fails to recognize the evil nature of the island's visitors.