Azkaban is a fictional setting from the Harry Potter Universe.
Azkaban is the wizarding prison. It is guarded by the Dementors and is virtually impossible to escape. If wizards or witches ever use one of the three Unforgivable Curses they will have a life-sentance here.
Azkaban was first mentioned in the second book where after the many attacks on Muggle-borns, Hagrid was accused again of being the Heir. They took him to Azkaban until Harry rescued Ginny from the Chamber. When he described it to Harry the following year, he said it was like there would be no more happiness in him anymore. In the third book, Sirius Black broke out of Azkaban.