The "mirror universe" is the informal name for a parallel universe, so named because many people and places are "opposites" of their counterparts in "our" universe, with "evil" replacing good and vice versa.
During the 22nd century, the capture of USS Defiant, a Starfleet vessel from a hundred years in the future, helped to solidify the Terran Empire's grip on power and dominance over the quadrant. (ENT: "In a Mirror, Darkly", "In a Mirror, Darkly, Part II")
The chance interaction between Starfleet officers from the primary universe during the 23rd century, with their counterparts from the mirror, who eventually led to the downfall of the Terran Empire and the rise of the Klingon-Cardassian Alliance. (TOS: "Mirror, Mirror"; DS9: "Crossover")