Imagine a society where everything has gone terribly, terribly wrong. Now write a novel about it. That's dystopian literature.
As opposed to utopian literature, dystopian literature presents a nightmare vision of the future. Dystopias are often warnings about society's current state of affairs and can offer critique of government and power.
Examples of dystopian literature include Margaret Atwood's The Handmaid's Tale, Aldous Huxley's Brave New World, and Lois Lowry's The Giver, which is an example of the genre's growing popularity in Young Adult literature.