Dementors are foul, rotting creatures that drain the happiness from people, feeding on their despair and their worst memories. They can suck out a person's soul through a process called the Dementor's Kiss. The Patronus Charm will give protection from the effects of a Dementor, but to drive a Dementor away you need to perform a full body corporeal Patronus. They cannot be destroyed, though you can limit their numbers if you eradicate the conditions in which they multiply (i.e., despair and degradation).
Dementors were first seen and mentioned by name in Harry Potter and the Prisoner of Azkaban by Remus Lupin, when explaing to Harry what had searched the train. However the first reference to them as the fearsome guards of Azkaban was made by Lucius Malfoy to taunt the soon to be arrested Hagrid.