A transporter accident sends Kirk and others to a brutal parallel universe where the Federation is an empire.
A transporter accident during an ion storm sends Kirk, McCoy, Scotty and Uhura to a parallel universe where the Enterprise belongs to a brutal Terran Empire. Officers advance by assassination, and Spock has a beard. The landing party must find a way home while pretending to belong.
This is the origin of the Mirror Universe, which Trek returned to again and again in later series. Fans enjoy the dark counterparts of the crew and the sharp costumes. Spock's decision to help Kirk change the empire is a key moment of hope in the story.