|You know it makes sense|
In the episode "Mirror, Mirror" (TOS) four characters (Kirk, Scotty, McCoy and Uhura) find themselves switched with their alter egos in a parallel "Mirror" universe. This second universe seems physically almost identical, but the society there is violent and cruel, with a ruthless Empire instead of the benevolent Federation. This is quite different from the divergent history sort of timeline. The worlds of "Parallels" diverged from a common reality in the recent past (for example, Captain Picard was rescued from the Borg, or wasn't). But the Mirror Universe could not be explained by a divergence unless it was many years ago, hundreds at least—the Empire and its society can't be a recent invention. In that case it's a bit surprising they arrive at a world with such curious similarities.
Later, Star Trek gave the Mirror Universe a history. But this was a mistake. It is really timeless. It's a dream world, come to life. It's the dark possibilities of reality brought out into the open. Everything is the same and yet horribly different. In Jungian terms we could say that it represents the Shadow. Star Trek is optimistic, or at least that was the original idea. The Mirror Universe is a negative image of the same world. That is why it is so fascinating.
One of its most interesting features is its curious and perverse attractiveness. Despite its horrors, the Enterprise of "Mirror, Mirror" is full of a barbaric vigour. Aggression rather than fear seems to be the dominant force. Brutal discipline of inferiors is matched by allowable assassination of superiors, and it is not like, say, real Stalinism. The officers are, a passing reference by Spock reveals, out for their own profit when engaged in missions, not just following the orders of the Empire.
The women of the Mirror Universe show a cool ruthlessness and aggressive sexuality. (See the video https://www.youtube.com/watch?v=HFuUTqdpduI Women of the Mirror Universe) In the ENT Mirror episode, Hoshi Sato (normally rather shy) is a femme fatale who is nobody's fool. It seems that relationships involve women in regular, but not permanent, partnerships, apparently governed by convention more than rules. Kirk finds Marlena Moreau, the "Captain's woman", living in his quarters. She feels their relationship is at an end and asks to be transferred. She isn't exactly a kept woman, though: the Captain's woman is a working officer. Also, there is apparently a close partnership between the Captain and Moreau. Mirror-Kirk had trusted her alone with his ultimate secret weapon. In the Enterprise portrayal of the Mirror Universe, it's a bit different, and the Captain's woman is much more out for herself. Or perhaps that's just Mirror-Hoshi, whose ambitions go all the way to the top.
What's more, it seems that Kirk's relationship with Marlena originally had its romance. Women aren't officially equal, as in the Federation, but they do have choices, and are active, indeed aggressive sexual actors. At the end of the episode, back in his own universe, Kirk meets the (Federation) Marlena Moreau. She seems far more vulnerable. It's interesting that Uhura, in impersonating her Mirror-universe equivalent, is more assertive and active than at any other point in TOS. The scene where she distracts Sulu is one of the great scenes of TOS. "I'm afraid I changed my mind again," she says sweetly after slapping him, backing off with dagger drawn. Viva Uhura!
In Robert Louis Stevenson's novel Dr Jekyll and Mr Hyde, Dr Jekyll finds a way to separate his dark side as Mr Hyde. But Mr Hyde eventually takes him over. The Mirror Universe characters aren't exactly the Mr Hyde versions of the usual Dr Jekylls, though, because there does seem to be more to them than evil. Mirror-Kirk and Marlena apparently had a romantic relationship at least to start. Mirror-Spock, despite the beard, has a degree of principle. This is necessary for the story, really: a world in which everyone was a hundred percent evil all the time would be as boring (for stories) as one in everyone was totally good all the time.
In "Mirror, Mirror", the details of the Mirror Universe are not spelt out in too much detail. You are left to work them out from the bits and pieces of information and comment, just like Kirk and companions trying to make sense of things. This is much more effective than telling the audience the facts. At one point, Mirror-Spock warns Sulu grimly that "my operatives would avenge my death... and some of them are Vulcans." Even the ruthless Sulu is frightened. So, Vulcan revenge would be...? Use your imagination. It'll be worse than anything they could have just told you. Or again, as I noted early, Spock to Kirk: "I have found you to be an excellent officer. Our missions together have been both successful and profitable." "Profitable." With just one word, an insight into a whole world. Subsequent visits to the Mirror Universe inevitably added more details, and the effect was to illuminate some of the shadows that had originally given the Mirror Universe such power.
Discipline in the Mirror Universe is brutal—the amiable Kyle is "agonized" for an alleged lapse in performance; not to mention the "agony booth" much better portrayed by Walter Koenig than in the later presentations. But this discipline doesn't seem to be very effective. Mirror-Sulu, leering at Uhura, shows indifference to his duties when not under the captain's eye. "When the cat's away..." he says. And that's important. The episode shows tyranny as not only unpleasant but ultimately ineffective and doomed to failure.
Somehow this vigour was never fully replicated overall in later versions, though particular aspects (such as Linda Park's portrayal of Hoshi Sato) were often excellent. Sometimes you have to wonder what they were thinking. The original "Mirror, Mirror" had colourful, flashy uniforms, with Uhura famously showing television's first belly-button. They apparently wear their medals all the time. In the Mirror Universe, if you've got it, flaunt it. But the ENT version's costumes seemed close to the drab ordinary uniforms.
Rather surprisingly, the Mirror Universe was not used in Star Trek: The Next Generation; a source of disappointment to fans. (There is however a superb Star Trek novel, Dark Mirror by Diane Duane, in which the TNG Enterprise meets its Mirror counterpart.) In Star Trek: Deep Space Nine it was re-introduced, but in a different form: its history had been derailed by Kirk's intervention and it no longer closely paralleled the main Star Trek world. The Empire had reformed and disarmed at the worst possible moment, and it had been conquered. Despite its major historical change of path, the Mirror Universe still consisted of exact analogues of the people in the main Star Trek universe.
These DS9 episodes were popular and made good use of the opportunity to get outside normal character and narrative limits. But it missed the point of the original Mirror Universe, by mixing up the negative mirror with the diverged timeline. The point of the Mirror Universe was that it was a mirror: a dark version of the same thing. The world of "Mirror, Mirror" was disturbing because everything is horribly wrong, yet almost the same. But now, the Mirror characters were placed in a different environment and set of relationships. Perhaps it's connected to the rather unusual and dark nature of DS9. A non-matching Mirror Universe is not out of place as one more dark aspect in the complicated dark narrative.
Incidentally, the history invented for the Empire post-Kirk may be considered a sign of the gradual falling away from the original ideals of Star Trek. A reformed, peaceful (and presumably more democratic) society is implicitly a weak society unable to confront threats. Perhaps you had better trust those militarists, unless you want to end up as a slave of the Cardassians. It's a standard method of authoritarian rulers to push the idea that only they can protect you from the enemies out there. (This theme also missed the point made in "Mirror, Mirror" that the vicious Empire was not actually very efficient, and that according to Spock its collapse was inevitable.)
The portrayal in Discovery gave a contemporary slant to the significance of the Mirror Universe by emphasising its xenophobic and racist nature; though curiously it seems to have lost its sexism.
Some fans have suggested that it's actually the Mirror Universe that is our own future: it's the benevolent Federation that's an alternative timeline.
Although the Mirror universe as we know it is a Star Trek thing, similar ideas had appeared in SF before. For example, in C.S. Lewis's unfinished novel The Dark Tower, the characters use a "chronoscope" to observe an "Othertime". It seems to be the same place, and they think (at first) it is either the future or the past. There is a large building which they eventually recognize as a replica of one close to them in their own time, so they think perhaps it's the future and the building is a replica. However, the events they're watching become weirdly unpleasant, and then they see a duplicate of one of their number, Scudamour, who evidently holds a powerful position there. He unintentionally crosses over, somehow changing places with his alter ego... By the way, it's disputed if the novel is actually by C.S. Lewis, but that's not important right now.
There is also a Brian Aldiss story "The Small Betraying Detail" (1965) in which the protagonist apparently slips into another world: "a world totally, horribly different from ours" might seem almost the same, apart from a "small betraying detail."
Ray Bradbury's classic short story "A Sound of Thunder" is of course based on a changed timeline. However it gains much of its power from the same sense of the combination of the ordinary and the changed. The unfortunate Eckels returns from the past, where he has accidentally killed a butterfly, and everything seems the same except that everything seems subliminally wrong.... What Bradbury describes is close to the Mirror Universe's sense of wrongness, which disturbs precisely because it is in familiar form. But here it is in fact much closer to the sensations of nightmare.
By the way, "Mirror, Mirror" was written by the science fiction writer Jerome Bixby, the author of an all-time classic SF short story "It's a Good Life". He also contributed other TOS episodes.