The wizard prison.  It is not known whether this is the only prison in the Magical world, but it certainly is the primary one for the British Isles.  It is located in the north of the North Sea. A very cold sea. (Interview with J.K. Rowling on Scholastic’s website.)

The primary guards at Azkaban are Dementors, tall thin skeletan type creatures covered in rotting flesh.  They have no eyes.  They drain humans of happy thoughts and live on human emotions.  They cause humans to see their worst memories.  Protection is through casting of the Patronis spell.  After an encounter, chocolate is a wonderful pick-me-up.

Dementors can also perform the Dementor's Kiss, it drains the soul out of body, leaving it alive, but without a soul.  They are supposed to do this only on orders of the Ministry of Magic, but they are not always controllable.  (See III - Chapter x)

Dementors are also known supporters of You-Know-Who.

The fastest way to end up in Azkaban is to use one of the Three Unforgivable Spells or to commit murder through another means.

Hagrid served a short stay here under suspicion that he had opened the Chamber of Secrets in Hogwarts for the second time.  His innocence was determined in Book II.

Sirius Black served many years, though innocent, before escaping by assuming the form of his Animagus. (Book III)

Bartholomew Crouch, Jr, also spent a year or so there before escaping with the help of his mother’s ultimate sacrifice. (Book IV)

XXX, Headmaster at Durmstrang, was a supporter of Voldemort and managed to bargain his way out by providing names of other Death Eaters.

Others known to be incarcerated there include many supporters of He who must not be named.