Welcome back to "Doggerel," where I ramble on about words and phrases that are misused, abused, or just plain meaningless.
I've read Flatland and Sphereland. I recommend you read them, too, if you've been overly contaminated by the typical sci-fi use of the term. A lot of woos are. I think "dimension" is a poor term for alternate universes, elseworlds, different planes of existence, etcetera. "Dimension" better refers to height, width, depth, time, and the various dimensions those cosmologists are working on. I heard we're up to ten or so. If you want to add some more, show us the math.
In the old days, religion liked to hide heaven in the sky and hell deep underground. Now that we can examine those areas, some woos have resorted to hiding magic in alleged dimensions. Of course, that doesn't change the fact that their woo doesn't do what they claim it does. It only serves to make it look harder to verify, as if science only worked like sci-fi scanning devices and was so easily limited.
Another use of the term is less "scientific" and more illustrative, often dealing with convenient abstractions for complex processes. One example, from my days of playing Magic: The Gathering was "card advantage," which essentially dealt with the benefits of increasing the number of cards working for you at any time: Draw more, prevent your opponent from drawing, kill two enemy cards with one of yours, etcetera. That's one aspect of a complex process. Though I've encountered it less often, sometimes woos like to talk about these sorts of dimensions to make an issue appear more complex when such dimensions can be studied independently of others.