A reality that exists alongside the familiar one, with its own version of history and often its own counterparts of known people, an idea Star Trek has explored from the mirror universe onwards.
A parallel universe is a complete reality separate from the one in which most of Star Trek takes place. Some differ in their physics, others only in the choices their inhabitants have made.
The Original Series introduces two in 2267: the antimatter universe of The Alternative Factor and the brutal mirror universe of Mirror, Mirror, to which Deep Space Nine, Enterprise and Discovery all return.
The Next Generation's Parallels presents the idea in its fullest form, as Worf slips between countless quantum realities in which every possible outcome has happened, each identifiable by its own quantum signature. Voyager meets Species 8472 in fluidic space, a universe filled with liquid, and the films beginning with Star Trek in 2009 are set in the Kelvin timeline, an alternate reality created by Nero's arrival from the future.