How is this novel an example of a dystopia?
Brave New World, by Aldous Huxley is a dystopia, because it is a novel about a society where the leaders believe they have created a perfect world (a utopia).
This particular "utopia" is such (according to its leaders) because no one has to deal with stress, pain, or anxiety (they take soma to take "vacations" from their problems); no one has to do work they don't want to do (hypnopeadia or sleep teaching instructs and conditions people to like the work they have to do); no one is denied pleasure (not only is promescuity accepted, it is encouraged); and no one is poor, lonely, or unhappy. Their every need is taken care of by the government....which is what makes this a dystopia.
The prefix "dys", means "away from". So a dystopia...is something that has fallen away from its intended purpose. Yes, the government provided everything for its citizens, but in so doing, it took away their freedom to choose...and freedom is a value that most human beings cherish dearly. Most wars are fought over freedom; the ability to choose for ourselves what our lives will look like.
The character John, from the novel, perhaps summed it up the best in his quote:
"But I don't want comfort. I want God, I want poetry, I want real danger, I want freedom, I want goodness. I want sin."
"In fact," said Mustapha Mond, "you're claiming the right to be unhappy."
"All right then," said the Savage defiantly, "I'm claiming the right to be unhappy."