The Third Reich (third empire) is a semi-anglification of "Das Dritte Reich", the term used to describe Germany under the Nazi regime. Sometimes also referred to as the Thousand Year Reich, as it was intend by its founder, Adolf Hitler, to stand for 1000 years. The "First Reich" was supposed to be the Holy Roman Empire, the "Second Reich" the German empire from 1871 to 1919.
Hitler very self-consciously tried to align his movement with great successes of the past which would resonate within the German people, and he definitely intended that his creation would bring his name and image to the whole world for 1000 years, so both terms were used repeatedly to build this sense of history, strength and inevitability in the minds of all Germans.
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, the Third Reich lasted only 13 years, from 1933 until 1945 (see Nazi Germany).