The Third Reich

The Nazis used the term "Third Reich" to mean, literally, the third empire of the Germans. The First Reich, according to Nazis, was in the Middle Ages. Hitler often referenced the Teutonic heritage of the Germans in speeches and in private. The Second Reich was the German Empire from 1871 to Germany's defeat in WWI, in 1918.

Encyclopedia Britannica:

Official Nazi designation for the regime in Germany (q.v.) from January 1933 to May 1945, as the presumed successor of the medieval and early modern Holy Roman Empire of 800 to 1806 (the First Reich) and the German Empire from 1871 to 1918 (the Second Reich).

Reich etymology according to Wikipedia:

Reich is the German word used most for "empire", "realm", or "nation" cognate with Scandinavian rike/rige, Dutch: rijk, Sanskrit: raj and English: -ric as found in bishopric. It is the word traditionally used for a variety of sovereign entities, including Germany in many periods of its history. It is also found in the compound Königreich, "kingdom", and in the country names Frankreich (France, literally the "Realm of the Franks"), Österreich (Austria, the "Eastern Realm") and Sverige (Sweden, the "Realm of the Suiones"). The German version of the Lord's Prayer uses the words Dein Reich komme for "ἐλθέτω ἡ βασιλεία σου" (usually translated as "thy kingdom come" in English), and the Lord's Prayer in Scandinavian also uses the cognate word.

Used adjectivally, reich is the German word for "rich". Like its Latin counterpart, imperium, Reich does not necessarily connote a monarchy; the Weimar Republic and Nazi Germany continued to use the name Deutsches Reich.