A term used both "in game" and "out of game", yet meaning roughly the same thing.
Inside the Star Trek Universe, alternate realities can be created via time travel altering the main time line, or they may exist independently.
Alternate universes are shed like skin flakes, "The Garden of Forking Paths" every point of decision exists in each possible form. There exists a universe where you didn't have coffee Tuesday morning. Now some branches of physics hold that these "quantum echoes" that have no significant differences fade back into the time line that created them. The number of alternate universes is infinite and ever changing. Time lines are shed at each and every point of decision. The universe vibrates with decision and from the outside would seem to be unfocused images of itself. Sort of like a video of a guitar string in motion. Some vibrate out of sync long enough to separate and you have a lasting alternate universe. Most have no significant effect and the quantum variation melds back into the parent line.
Each decision you and every part of the universe that can make decisions makes sets the universe vibrating with alternate possibles. A large enough vibration creates another universe.
The end result is there is no such thing as a core or "pure" time line. All are equally valid. The problem with time travel is you do not move solely up and down the time stream, it does not work that way. Time travel is alternate universe travel. Indeed the minute you insert yourself into a past time line you create an alternate universe by your very presence. The mutability of the universe and the nature of alternate universes are the only reason time travel does work. You never get back to the universe you left. There will be differences either minor or even significant. Those that build dedicated time machines learn this to their grief. You cannot go home again. Dwelling too long on the total mutability of the seemingly immutable universe has been known to drive people insane. The study of Hyper-dimensional physics requires the applicant pass a battery of tests for mental stability. That way lies madness.
A few species, notably Ane can handle this concept without qualms. Psychologists credit the psionic ability to teleport with this stability in the face of the "impossible". The manner in which the Ane teleport functions means that Ane are wired to understand and navigate the Hyper-dimensional space. Most cannot explain it to you however. It is rather the centipede's dilemma. They just do it, they can't explain how.
In Epiphany Trek the mirror universe is not "real". It is a quantum reflection caused by the stress on space time. Study of the various events have proven that the mirror universe parallels the prime universe far too closely for the apparent differences that are seen. Divergence should be frequent and drastic. That is not the case. When ever the mirror universe is encountered it parallels the people and events currently happening in the prime universe.
Expanded article on the Mirror Universe
In terms of writing and world building, a fanfic writer may rewrite certain events in Trek history, or certain "rules" of the Star Trek Universe. An easy example is phasers. Some technical sources, and even canon episodes state that phasers cannot be fired at warp, presumably because the phaser beam moves at the speed of light. However, there are numerous occasions where during episodes, phasers other beam weapons are fired at warp speed.
A fanfic writer who elects to limit phaser fire in his stories to "sublight only" may be more internally consistent, but has differentiated his setting from the canon. The inconsistency of the rules governing Star Trek's imaginary physics and technology is legendary
Some writers add characters, races, worlds, cultures and even entire stellar empires to their Trek fanfics or RPG settings. When they do, the result is an alternate universe.