Germany was a pre-War European country. After World War II, the country was divided into three distinct states, the German Democratic Republic (East Germany), the Federal Republic of Germany; (West Germany) and the Republic of Austria. By 2060, as the European Commonwealth dissolved, the country fell into disarray, bickering and quarreling with its neighbors over the last few remaining resources on Earth. As the picture of a destroyed Reichstag in the Fallout intro implies, full-out war broke out between the former allies.
Little is known about the country in-game outside the above references, although the presence of Gauss rifles in mainland United States in copious amounts as well as employment of a strikingly similar weapon system by the Chinese implies the Germans had equal opportunity business deals with both sides of the Great War.