Unknown Location in Continental Europe
Gellert Grindelwald (prisoner)
Nurmengard is a wizarding prison possibly near Germany or Bulgaria. In terms of magical defences, its specific protective enchantments remain unknown, but it is known to have anti-Apparition wards (similar to Hogwarts). Non-magical defences include high walls for the fortress, and it may have had a guard population, similar to Dementors once guarding Azkaban (though was implied to have since become disused and automated without the need for a human presence).
The prison was built on the orders of the Dark Wizard Gellert Grindelwald at the height of his power, in order to hold his opponents. Grindelwald's slogan "For the Greater Good" is carved over the prison's entrance. After a number of years terrorising Europe, Grindelwald was confronted and defeated by his former best friend, Albus Dumbledore.
In a display of irony Grindelwald was collared in the top-most cell inside his own prison, rather than killed, after his defeat. It is unknown if there were any other prisoners ever held at Nurmengard but around the time of Grindelwald's death, it is highly likely that he was the only prisoner present; all other past inmates having been incarcerated at the ex-Dark Lord's behest.
Quest for the Elder Wand
In his quest for the Elder Wand, Lord Voldemort travelled to Nurmengard in 1998, using his ability to fly to break into Grindelwald's cell. After confronting him for information on the Wand's location, Voldemort killed Grindelwald, and then flew away.
It is described as being "a towering building," and a "grim fortress, jet black and forbidding,". The cell that was inhabited by Gellert Grindelwald since 1945 had been a dark and ominous room in the highest tower, with a stone bed and a ragged, thin blanket.
Nurmengard may be a reference to Nuremberg, the city in Germany that was the site of many important Nazi rallies, and also the place where the anti-Semitic Nuremberg Laws were promulgated. Later the city was famous as the site of the prison used to hold infamous Nazi war criminals, and the Nuremberg Trials where they were tried for war crimes and crimes against humanity. Likewise, Nurmengard was created as a monument to Grindelwald's oppressive regime, but later became a symbol of his downfall.
The suffix "-gard" comes from the Norse "gard," meaning "enclosure" or "walled town." Also, in French, "garder" means "to keep, ward, guard, save, preserve".
J.R.R. Tolkien used a similar word for his place names in Middle-earth when referring to enclosed spaces; for instance, the fortress of the dark wizard Saruman is named Isengard meaning literally "iron fortress." Isengard was built by the people of Numenor, so the first two syllables of Numenor and the last one of Isengard would be Numengard. It is possible that J.K. Rowling did not read Tolkien's Legendarium, written a few decades ago, but it is more likely that the 'gard' part was more of a coincedence than 'Numen.'
"The greater good" is an essential idea of the utilitarian philosophy. "For The Greater Good" may also be a reference to "Arbeit macht frei" (German, "Work makes free" or "Work liberates") the motto that was mendaciously inscribed over the entrance gates to several Nazi concentration camps (The exact wording of the inscription at Nurmengard is unknown, since Grindelwald's exact nationality or his language of preference, are not specified in the books; the German translation of his slogan would be "Für das höhere Wohl").