Huxley's title is of course a quotation from Shakespeare (The Tempest), so I think one has to start there.
Here is one explanation of it:
The phrase originated with Shakespeare. When he put the expression in Miranda’s mouth in The Tempest, he was being ironic.
How many goodly creatures are there here!
How beauteous mankind is! O brave new world,
That has such people in’t!
Miranda is speaking of the men whom her father—Prospero, rightful Duke of Milan— has caused to be shipwrecked on their island. The irony is that five of the eight men who come ashore are not “goodly” at all; they are dirty rotten scoundrels who represent all that is evil and corrupt in the “civilized” world of Europe.
When Aldous Huxley chose the phrase as the title of his 1932 novel about a future in which society is carefully organized and monitored, he was echoing the idea that what might appear to be wondrous at first glance may in fact be evil.
In Shakespeare’s day brave could mean splendid, showy, grand, fine, and handsome*. Miranda, impressed by the appearance of the courtly strangers, was probably using the word with this meaning.