Dimension refers to a quality of measurement, specifically how many coordinates are required to locate something at a specific place in space. Normal locations require three dimensions to be defined, in addition to the requirement of knowing at what point in time a given location is being observed. Scientific theory and mathematics have posited additional dimensions which exist as extensions of the space-time continuum, with additional parameters of measuring those dimensions that do not exist in the universe, giving them qualities of separate universes.
It has been proven that continuums can connect through using means to transcend additional dimensions. A group of two-dimensional lifeforms that could only exist in a plane of their dimensional reality which somehow intersected Federation space in the year 2367. The starship Enterprise-D became ensnared in the lifeforms and their plane, specifically interfering with the empathic powers of Counselor Deanna Troi. (TNG episode: "The Loss")
Dimensional feedback is an energy phenomenon which can affect objects that travel outside of a normal timestream or dimensional space. This effect can interfere with the proper navigation of certain types of time travel technology. (TNG - Assimilation² comic: "Issue 1")