In the Harry Potter books, the prison guarded by Dementors is Azkaban.
Azkaban is the wizarding prison used by the Ministry of Magic to hold convicted criminals. It is located on an island and is guarded by Dementors, beings that feed on positive emotions and leave prisoners overwhelmed by despair. Their presence makes imprisonment especially traumatic.
The prison is central to the backstory of Sirius Black, who escapes after being imprisoned for crimes he did not commit. It also appears in the histories of other witches and wizards involved in the First Wizarding War and Voldemort’s return.
Azkaban should not be confused with Nurmengard, another prison connected to the dark wizard Gellert Grindelwald. Gringotts is the wizarding bank in Diagon Alley, while Durmstrang is a magical school. The name Azkaban is used for the prison itself, not for the Dementors who guard it.