A reich ( /ˈraɪx/; ) is one of the three major German empires that have existed, particularly Nazi Germany. The First Reich was the Holy Roman Empire, which lasted from the 10th century until 1806. The Second Reich was the Hohenzollern Empire, which lasted from 1871 to 1918. The Third Reich was Nazi Germany, which lasted from 1933 to 1945. The concept of the three major reichs was important in Nazi ideology as part of the general premise that the German people were destined for greatness.
The term reich derives from the German word meaning realm, kingdom, or empire. It is a word cognate with the English word rich with the same meaning as an adjective, but more importantly its homonym as a noun, Reich, is usually used in German to designate a kingdom or an empire and also the Roman Empire. The terms Kaisertum and Kaiserreich are used in German to more specifically define an empire led by an emperor. To some extent Reich is comparable in meaning and development to the English word realm (via French reaume "kingdom" from Latin regalis "royal").
In the case of the Hohenzollern Empire (1871-1918), the official name was Deutsches Reich, is literally translated as "German Realm", because formally the official position of its head of state, in the Constitution of the German Empire, was a "presidency" of a confederation of German states led by the King of Prussia. He assumed the title of "German Emperor" (Deutscher Kaiser), which rather referred to the German nation than directly to the "country" of Germany.
The Latin etymological counterpart of Reich is not imperium, but rather regnum. Both terms translate to "rule, sovereignty, government", usually of monarchs (kings or emperors), but also of gods, and of the Christian God. 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) Himmelreich is the German term for the concept of "kingdom of heaven".
Except for its Latin cognate regnum (kingdom) it is cognate with Scandinavian rike/rige, Dutch: rijk, Sanskrit: raj and English: -ric, as found in bishopric.
Read more about Reich: Etymology