German is the main language of Austria, and Austria has played an integral role in the history of Germany for centuries. Germany wasn't always a united nation-state. It used to be fragmented principalities, bishoprics, duchies, counties, marches, and so forth. Austria was just one of these. Austria is a separate country today because the former Holy Roman emperers, the Habsburgs, held Austria, Hungary, and other lands outside the Empire. Thus, when the rest of Germany was beginning to coalesce under the leadership of Prussia, the Austrian emperor (and king of Hungary) had other business. Of course, the Austro-Hungarian Empire eventually collapsed into Austria, Hungary, Yugoslavia, and Czechoslovakia (roughly); but, by then, Germany was firmly established as its own loose empire, with the king of Prussia becoming the German kaiser.
It is only the result of different allegiances between the feudal princes that the Netherlands, Switzerland, Liechtenstein, Luxumbourg, and Austria aren't one German nation-state today. Remember that, in much of northern Germany, the language spoken wasn't so different from the Low Franconian dialect that became Dutch. However, Low German (low as in near the sea) was eventually replaced by High German (Hochdeutsch), which largely became the standardized form of German because the Gutenberg Bible was written in that dialect (before then, Latin was the authoritative language in Germany).
The linguistic situation is similar to what France's was before the twentieth century. The language of southern France, Occitan or the langue d'oc, was widely spoken in the Provençal countryside until centralized school administrators decided that, to better unite France as a nation, everyone should speak like a Parisian. Occitan is actually more closely related to Catalan, Spanish, and Italian than it is to French.