Durmstrang does not really mean anything in German although it sounds very German, but if you switch the beginning letters of each syllable it says sturm-drang, and Sturm und Drang is the name of a period in German literature around 1770. It is in this period that the dark, brooding, romantic hero of European literature is born. This character-type is reflected in Victor Krum from Durmstrang.
Sturm und Drang, or Storm and Stress, was a movement in German literature that flourished from c.1770 to c.1784. It takes its name from a play by F. M. von Klinger, Sturm und Drang (1776).
headmaster: Igor Karkaroff
location: a castle in northern Europe, so far north that the days are very short in winter
uniforms: furs, blood-red robes
notes: The Durmstrang Castle is not as big as Hogwarts, having only four floors. Its fires are only lit for magical purposes. The grounds are quite extensive and include lakes and mountains. Durmstrang has the reputation of teaching Dark Arts. It does not admit Muggle-born students.
Durmstrang is the hardest of the schools to place. We know that Victor Krum, their Triwizard Champion, is from Bulgaria (he plays on their national Quidditch team and he speaks Bulgarian with his parents), the name of the school sounds German, and the names of the Headmaster, Igor Karkaroff, and the only other student that is mentioned by name, Poliakoff, sound Russian. Viktor Krum tells that in winter they have very little daylight which indicates that the school must be situated in a place far north, near the Arctic circle. This is also supported by the fact that the students wear fur capes as part of their uniform. The school is thus placed in a cold arctic region of eastern Europe which leads the thought to the North-Eastern Part of Russia. Most guess it would be Germany, since durm and strang are German words.
On the one hand, German continues to be sort of a "lingua franca" (a common language) in a lot of Eastern Europe; this is a relic of the days when most of the cities and towns were mainly German-speaking, and Slavic, Romanian and Magyar were the dialects of peasants. For a long, long time, up till the end of WWII, a lot of the professional classes and middle-classes in Eastern and Southeastern Europe were German-speaking, On the other hand, the only Durmstrang types we get to meet have Slavic-sounding names
Durmstrang could require that students coming in from backgrounds that do not speak the language of instruction must first master at least enough of Durmstrang's language of instruction to be able to follow along in lessons, even if they speak with horrendous accents.