Prior to the unification of Germany, the House of Hohenzollern had held the Prussian throne for some time and had also been electors of the Holy Roman Emperor. William of Hohenzollern was also William (spelled Wilhelm) first of Prussia. His chief minister was Otto von Bismarck. Bismarck through a series of machinations, managed to have Germany united under Prussian leadership. He did so by a series of wars which appealed to German nationalism. Wilhelm I of Prussia became Kaiser Wilhelm I of the German Empire when he was crowned at Versailles. Kaiser, of course, was the German equivalent of "Caesar." He was succeeded later by his son Wilhelm II who was the last Kaiser. He abdicated at the end of World War I and lived the rest of his days in Switzerland.
There actually was no true German monarchy; but there were two German Emperors, both of them Hohenzollern.
Germany was only a monarchy (as a united country) for a very short time. The German monarchy lasted only from the unification of the country in 1871 to the end of World War I in 1918. During this whole time, the monarchs were from the House of Hohenzollern. The Hohenzollerns were the hereditary monarchs of Prussia before unification. Because Prussia was the strongest and most important of the states that made up unified Germany, the Hohenzollerns became the ruling family of Germany when it unified. So, the Hohenzollern dynasty is related to the German monarchy by the fact that the German monarchs were from that dynasty.