Why did Hitler call his government the Third Reich?
The use of the phrase "Third Reich" was intended to connote a sense of connection with the past, particularly the German past. The first "reich" was the Holy Roman Empire, which lasted hundreds of years beginning with the crowning of Charlemagne as Holy Roman Emperor in 800. Charlemagne was a Frankish king, and the Franks were a Germanic people. His rule brought several German principalities and fiefdoms together, if only nominally. The Second Reich refers to the German Empire established in 1870 through the machinations of Otto von Bismarck and under the rule of the Prussian Hohenzollern rulers. This "reich" lasted until the end of World War I, when Kaiser Wilhelm II abdicated in the face of defeat. The first two "reichs" were thus moments of perceived or remembered German unity, and Hitler and his propagandists sought to assert legitimacy for the emerging totalitarian state by framing it as essentially the culmination of centuries of German history. This fit squarely within Hitler's highly radicalized, mythological view of history, which asserted that the German people, as racially superior "Aryans," were destined to rule Europe and the world. His dream that the Third Reich was destined to be a "thousand-year" Reich was dashed, as it came crashing down with German defeat in World War II.
"Reich" meant something along the lines of "kingdom" or "empire." The Nazi mythology was that theirs was the third truly German kingdom that had existed in the world.
The first was the Holy Roman Empire which existed back in medieval times. The second was the Germany that existed from the time that the country was unified (1871) until the end of WWI.
(This comes from the link below, which copied it from Encyclopedia Britannica's entry entitled "Third Reich.")
The Nazis called their regime this to emphasize that it was a purely Germany government and to give it historical legitimacy -- to make it seem like it was connected to these previous empires.
Third Reich meaning third empire in German language was supposed to represent the rule of Hitler in Germany as the beginning of the third great empire to last for a thousand years, the first two empires being Holy Roman Empire (First Reich) and the German empire under Hohenzollern dynasty (Second Reich) achieved by Bismarck.
On august 19, 1934 a plebiscite put to German people decided overwhelmingly in favour of making Hitler a head of state as Fuhrer (leader) and Reich Chancellor. At the party Rally in Nuremberg, following this victory, Hitler declared that Nazi revolution was complete and and in next thousand years there will be no other revolution in Germany. Thus began the concept of Third Reich which was supposed to last for thousand years.
For further detail please refer to the link given below.