The Third Reich is an anglification of the German expression "Das Dritte Reich", and is used as a synonym for Nazi Germany. The term was introduced by Nazi propaganda, which counted the Holy Roman Empire as the first Reich, the 1871 German Empire the second, and its own regime as the third. This was done in order to suggest a return to alleged former German glory after the perceived failure of the 1919 Weimar Republic.
The Third Reich was sometimes also referred to as the "Thousand Year Reich", as it was intended by its founder, Adolf Hitler, to stand for one thousand years.
Thus the Nazi Party used the terms "Third Reich" and "Thousand Year Reich" to connect the allegedly glorious past to its supposedly glorious future.
Initially Hitler's plans seemed to be well on their way to fruition. At its height, the Third Reich controlled the greater part of Europe. However, due to the defeat by the Allied powers in World War II, the Thousand Year Reich in fact lasted only 12 years (from 1933 through to 1945).
See also: millennialism.