A transporter mishap sends Kirk, McCoy, Scotty, and Uhura to a parallel universe where the benevolent Federation is replaced by an evil empire, in which torture is commonplace, crew members advance through the ranks by assassinating their superior officers, and Spock has a goatee.
What's more, the evil versions of Kirk & Co. have been transported to the good version of the Enterprise.
In addition to introducing the now-timeless "goatee signifies evil twin" trope, Mirror, Mirror was the first episode to suggest the existence of alternative timelines to the Star Trek universe, an idea that formed the basis of J.J. Abram's 2009 reboot of the franshise.