They guard the prison of Azkaban. They suck all the happiness out of people and you'll feel like you'd never be happy again when a dementor comes near you.
"Dementors are among the foulest creatures that walk this earth. They infest the darkest, filthiest places, they glory in decay and despair, they drain peace, hope, and happiness out of the air around them. Even Muggles feel their presence, though they can't see them. Get too near a dementor and every good feeling, every happy memory will be sucked out of you. If it can, the dementor will feed on you long enough to reduce you to something like itself...soul-less and evil. You will be left with nothing but the worst experiences of your life."