Few things love I more than German history! Allow me to help:

Before I go into a long lecture, here's the tl;dr version: First Reich means Holy Roman Empire; Second Reich means German Empire or Kaisserreich. If you want details on what those mean, please continue. I’ll give a (for reddit, though still a Berlin Text Wall) brief historical overview of both.

Reich, usually translated as “empire” though really means “realm”, is a common feature in German names for states (countries). For example, German for France is “Frankreich”, literally “Realm of the Franks”, the name of the Germanic people which settled in then Roman Gaul and from which the name France itself is derived. That aside, the so called “Reichs” of which you speak are considered to be the three German empires of history. The first was “Das heilige römische Reich (der deutsche Nation)” or “The Holy Roman Empire (of the German Nation)”. The French thinker Voltaire once quipped that the “Holy Roman Empire was neither holy, nor Roman, nor an empire”. But I’ll get to that in a bit. The second Reich was the Kaiserreich (literally “Realm of the Emperor”).

The Holy Roman Empire of the German Nation (HRE) was never much of an empire in terms of political organization. There was a Kaiser (emperor) throughout its existence, but the Kaiser never had the same level of political control over the realm as other emperors or kings; the various member states, such as Bavaria or Austria, had greater autonomy throughout most of its history than other sub-national entities in other empires or kingdoms. The founding of the HRE is somewhat up for debate: Karl der Große, or Charlemagne as he is called in English and French, was king of the Franks. His kingdom stretched across modern day France, BENELUX, and most of Germany, as well as other lands. Karl is often considered to be the father of both France and Germany. When he died in 814, his kingdom was divided among his heirs into three parts. One part is the beginning of what became France, while another is where we see Germany beginning (though, Germany’s history is much more complex than France’s, insofar as how we came to a single German state vs. how we came to have a single French state; another topic for another AskHistorians post!).

On 25. December, 800, Pope Leo III crowned Karl “Imperator Romanorum” or “Emperor of the Romans”. Thus, we get the name “Holy Roman Empire”, though that name itself was not used for several hundred more years. Holy should be obvious, as the Catholic Church bestowed the title, for various reasons; among them being it was intended to delegitimize the Byzantine Empire as the successor state to the Roman Empire and establish Rome firmly as the center of Christendom rather than Constantinople. This notion of the Roman successor state is where Roman comes from. Realm or Empire refers to the state itself. Later, “of the German Nation” was added since most of the realm was Germanic (look at a map from any point in its history; the Reich mostly corresponds to present day Germany, Austria, Switzerland, and Netherlands).

Still, 800 is where we trace the imperial title, and thus we can consider this the start date of the so called First Reich. Another state date would be 2. February, 962, when Otto I was crowned Kaiser. He revived this title, which had gone some 60 years unused. The title was used from Otto I through to the official end of the HRE in 1806, when the last bearer of the title, Franz II of the House of Habsburg, abdicated the title. See the Napoleonic Wars for more details on that. From Otto I through to the 1300s or so, the Kaiser had a greater amount of political control we may think of when we hear king or emperor as a title. In the 1300s, the power of the Kaiser waned and the various states within the empire took on greater power and autonomy. This is, perhaps, best shown in the rivalry between the Kingdom of Prussia and Habsburg Austria in the 1700s. Parts of both states were in the HRE and both vied to be the primary German state, including after the “fall” of the HRE.

So what about the Second Reich? Well, skipping ahead from 1806 to the 1860s, we see some faces you may know from history classes or certain popular video games (e.g. Sid Meier’s Civilization series). Perhaps most important of these is a Prussian politician named Otto von Bismarck. Bismarck is largely responsible for the creation of a truly German state, or “Germany”. You see, Germany is a rather young country, insofar as being a unified state. France, England, Russia, Spain—many countries were founded long before Germany became a unified state. Even the USA is older. Prior to 1871, Germany existed as a term and a concept, but it never materialized. It wasn’t until Otto von Bismarck, Prussian King Wilhelm I, and an assorted cast of politicians and military leaders put plans in motion for a series of wars that led to the creation of a single, unified Germany.

Bismarck, et al., orchestrated a trio of wars called the German unification wars. These wars had several purposes: gain territory or influence for Prussia from rival states; convince smaller German states to support Prussia for German dominance rather than Austria; and to beat the key German rivals so as to make Germany a leading force in Europe, rivaling the traditional great powers like France or the UK. The three wars were: the Danish-Prussian War of 1864, the Austro-Prussian War of 1866; and the Franco-Prussian War of 1870-71. On 18. January, 1871 the Prussian King was crowned Kaiser Wilhelm I and the German Empire (2nd Reich) was declared in Versailles. The Prussian-led German coalition had trounced France and Napoleon III, taking Paris, days before. The 18th of January was the anniversary of the founding of the Kingdom of Prussia in 1701, so the Reich was declared for the anniversary. The newly declared Reich went on to defeat the French Republic, declared in the aftermath of Napoleon III’s defeat, a few months later. Wilhelm I died years later, with his son, Friedrich III, briefly holding the title, before Friedrich’s son became Kaiser Wilhelm II, best known for Germany’s involvement in World War I. Germany was defeated in 1918, Wilhelm II abdicated and fled to the Netherlands, the Weimar Republic was declared, and so ended the 2nd Reich. Enter stage right one Adolf Hitler and the 3rd Reich.

And so ends my history lecture! I hope this has been helpful! If you would like any further information/have follow up questions, ask and ye shall receive!

By the way, I am very specific with certain terms when discussing German history: I always use “unification of Germany” to mean the foundation of the first German state, aka the Kaiserreich/Second Reich, while “re-unification of Germany” means the joining of the West and East Germanies in 1990.