Anyone who is vaguely familiar with World War II and the events that led up to it has almost certainly heard Nazi Germany referred to as "the Third Reich." The term is a literal translation of "das dritte Reich," the term the Nazis themselves coined to describe their administration of Germany. In this context, the word "Reich" is almost never translated into English, which I've always found really interesting. We know that there have to be at least three of them, but "Reich" is a word that has no intuitive or immediately obvious English equivalent. So what exactly is a Reich, and if the Nazis controlled the third one, what happened to the first two?
When the word "Reich" is used in non-Nazi contexts, it's usually translated as "Empire." The best-known example of this would be what we in English now call the Holy Roman Empire, which is rendered in German as das Heiliges Römisches Reich. This term is itself a translation of the Latin Sacrum Imperium Romanum, which means the same thing. The "Holy" qualifier was added to distinguish it from the original Roman Empire, known in German as das Römisches Reich and in Latin as Imperium Romanum. So should the Third Reich really be called the Third Empire?
Not exactly. Everyone is (hopefully) aware that not all words have exact equivalents in other languages. We also know that words can have their meanings change over time, which further compounds the problems in making one-to-one translations. A related example would be the Latin word "Imperator," which is the basis for the English word Emperor as well as related words in other languages (e.g., emperador in Spanish, empereur in French, etc.). "Imperator" was originally a title with a meaning similar to "field commander," and it is of course related to the previously mentioned word "Imperium," which originally meant "area of control."
Now at this point, you might be thinking "ok, but clearly there is a relationship between the concept of an 'empire' and an 'area of control.'" And you'd be correct! It is, however, a long jump from one to the other. "Imperium" could refer to the entire Roman Empire or it could also simply refer to one office-holder's particular area of responsibility. "Reich" is an adequate translation of the original meaning of "Imperium" in the sense that it means an area of control, but again, that's a far cry from an "empire" in the sense that we understand it today.
German, of course, is an Indo-European language. This is a massive language family that also includes English, Latin (and its descendants), Greek, Sanskrit, Farsi, and far too many others to list here. All of these languages ultimately derive from one proto-language that is helpfully called proto-Indo-European. Many Indo-European languages have words beginning with an R sound that refer in some way to power, authority, control, or related concepts. Obviously the German "Reich" is the most pertinent example, but others would include the Latin "Rex" or the Sanskrit "Raj." In modern English (by way of medieval French), we have a word that conveys a similar meaning to "Reich," which is "Realm" (and indeed, that is my preferred translation for the word "Reich"). Even that, however, is not perfect because the word "realm" implies something that is under royal (French "réal") control while a Reich does not necessarily need a king or queen. So even though I think "realm" is the best translation from a practical standpoint, let's get more pedantic!
I mentioned before that "Reich" is usually translated as "empire" in most non-Nazi contexts, so let's look at some other examples in German where it's not. The German word for France is "Frankreich," literally the Reich of the Franks (an ancient Germanic tribe that inhabited what we now call France after the fall of the Roman Empire in the West). The German word for Austria is "Österreich," the Eastern Reich. Even common nouns like Köningsreich (kingdom, literally "king's Reich") and Kaiserreich (empire, literally "emperor's Reich") use the word.
You'll also see forms of it in Germanic languages other than German: for example, the Swedish word for Sweden is Sverige, the Swede Reich while the official name of Norway in Norwegian is Kongeriket Norge, the Kingdom (King's Reich) of Norway. English is also a Germanic language, and believe it or not, there is one archaic word that has survived to modern times that retains the early English form of the word "Reich" in this context: bishopric, the area of a bishop's control. However, the word "ric" is obviously not in use in modern English, so while that's not going to work, there is one more word we should look at.
Modern English does in fact have a word related to "Reich" that deals with both geography and something within one's control, and that word is "Reach." It would be a somewhat more literary use of the word, e.g., "all this territory is within the king's reach," or something similar, but the meaning is clear. I know it's a little anti-climactic that we're just switching one letter in the word, but languages are like that sometimes, and I think there's probably a very old etymological relationship between the two words. For the record, though, I still think "realm" communicates the intended meaning of "Reich" the best out of any of the options so far.
So now we need to return to the question of why the Third Reich is (supposedly) the third. In German historiography, the aforementioned Holy Roman Empire is considered the First Reich. Voltaire famously quipped that the Holy Roman Empire was "neither Holy, nor Roman, nor an Empire," and while we can debate the intricacies of this statement all day long, the fact of the matter is that he was essentially correct in the sense that the nucleus of the HRE was located in the German-speaking lands of Europe rather than somewhere like, I don't know, Rome. The Holy Roman Empire received its name not because it claimed to be the reconstitution of the ancient Roman Empire but rather because it was set up as the successor to the supreme authority within Christendom that Rome formerly represented. Charlemagne was the first Western European ruler to be given the title of "Emperor" since the late 5th century, and his being crowned was the climax of a struggle between the papacy in Rome and the Byzantine Empress Irene in Constantinople (who also claimed to be the supreme authority within Christendom). Even Charlemagne was conflicted about receiving the title, vacillating between whether his title should be translated as the Roman Emperor, the Emperor of the Romans, or the Emperor of Rome (all of which imply different things).
Eventually, the question of who was Europe's supreme political authority became much more complicated and the focus moved to issues surrounding national identity. The Holy Roman Empire would later have its "official" name changed to the Holy Roman Empire of the German Nation, and it is for this reason that the HRE -- the first consolidation of Germanic power since the fall of Rome -- is considered the First Reich. The Holy Roman Empire would be dissolved in the wake of the French Revolution and the subsequent Napoleonic Wars, and there would be dozens of independent German polities. Now, granted, most of them were basically city-states without much significance to speak of, but after Napoleon's final defeat, a supra-national organization called the German Confederation was formed. The German Confederation was kind of like the Arab League or the Organization of American States today in that it was not a "government" or even a "state."
The two most powerful members of the German Confederation were Prussia and the Austro-Hungarian Empire, the latter of which considered itself the main successor to the Holy Roman Empire and therefore the rightful leader of the Confederation. Advocates for German unification into a single state considered two possibilities: the Greater German Solution, which would include Austria (and presumably Austrian leadership) and the Lesser German Solution, which would exclude Austria (and would instead entail Prussian leadership). The question was ultimately decided after the Seven Weeks' War which saw Prussia defeat Austria in 1866 and then the Franco-Prussian War of 1870-1871, in which Prussia and its allies defeated France. Afterwards, the German states (minus Austria and a few others like Switzerland) were unified into the Deutsches Kaiserreich, the German Empire, which is considered the Second Reich. (In much the same way that Charlemagne had wished to avoid making the wrong impression with his title of Holy Roman Emperor, Wilhelm I did not want to be proclaimed "German Emperor" in public, even though that was his constitutional title; he preferred "Emperor Wilhelm of the German Empire.")
You'll notice that both the First and the Second Reichs represent high points in the history of German political power as well as key moments of German unity. After Germany's defeat in World War I, the monarchy was abolished and the Empire was replaced by a parliamentary democracy. This period -- from 1918 to 1933 -- is generally called the Weimar Republic. When the Nazis came to power in 1933, Adolf Hitler proclaimed his Germany the Third Reich. The term "Weimar Republic" was coined by Hitler to denote what he considered the denigrated nature of the German government at that time (Weimar was the city where the provisional government was formed after the Kaiser was overthrown). Interestingly, the official name of Germany after the abolition of the Empire was simply the "Deutsches Reich," or the German Reich. The term "Third Reich," then, was Hitler's way of not just trying to associate his regime with the most significant expressions of German strength, but also his way of comparing the Weimar years to the weakness and chaos of the German-speaking world after the fall of the Holy Roman Empire. (As an aside, when the Nazis annexed Austria in 1938, the name was changed from Österreich to Ostmark, a very ancient name for Austria meaning "East Region;"
there could be only one "Reich," after all.)
For all intents and purposes, the word "Reich" can be adequately rendered as "realm" in English, especially as it relates to concepts like "Frankreich" or "Kaiserreich." However, when it comes to questions regarding German political history, there is something untranslatable in the word that relates to the intersection of power, ambition, centralization, and bellicosity. To an English-speaker, the word "Reich" has a harsh -- even menacing -- sound that makes it quintessentially Teutonic. "The Third Reich" conveys a sense of danger that just doesn't come across if we call it the Third Empire, the Third Realm, or the Third Reach.