Why was it the third?
“Reich” is German for “empire” or “realm.” Nazis believed they were the third great empire, after the Roman empire, and the first German empire.
The name was first used by Arthur Moeller in a 1923 book. Hitler popularized the name, which its assumed he found in Moeller’s works. I’m also assuming Moeller retroactively named the first and second Reichs to make the point that Nazi Germany was the third.
The “Fourth Reich” is sometimes used to discuss a potential resurgence of Nazi-ism.
Why I Looked It Up
I had obviously heard the term before, but didn’t understand the specific reference.