Dimension
From Memory Alpha, the free Star Trek reference.
In the field of basic physics, a dimension is described as one of the three basic directions an individual can travel from a specific point, namely: up/down, left/right, and forward/backward, with the fourth dimension being time. These four dimensions make up the realm of space.
It is believed that beyond the universe itself, few things, like other dimensions and higher levels of being exist. Unfortunately, during the 23rd century, the existence of these concepts could not be proven logically. (Star Trek: The Motion Picture)
The Androids of planet Mudd had an advanced understanding of dimensions, having formulated computations that would inevitably lead to a total description of the parabolic intersection of dimension with dimension. (TOS: "I, Mudd")
The mirror universe coexists with our universe, but on a different dimensional plane. (TOS: "Mirror, Mirror") It was later determined that the dimensional structure of each universe was totally dissimilar, and that any use of power would disturb its structure. (TOS: "The Tholian Web")
The galactic creation point extends through space and time into another dimension where the logic of things is totally different, where magic makes things go. (TAS: "The Magicks of Megas-Tu")
According to Spock, the negative universe occupies the same space, as our universe, but in different dimensions. (TAS: "The Counter-Clock Incident")
The planet Meridian has a dual existence, appearing in both the Gamma Quadrant of our universe, and another dimension that intersects with this one at that point. (DS9: "Meridian")
