Hyperspace is another "layer" (if that's the correct word) of space that, when compared to normal space, doesn't exactly follow a 1 to 1 ratio. For instance, if you enter hyperspace and go, say, 100 miles in hyperspace, and then exit, you won't be 100 miles from where you were originally. May end up being light years away. Hyperspace seems to have strange folds in it too.
As for any more details, I don't have a clue.
It has been theorized, however, that there are more than just 4 dimensions. We can't perceive them, of course. They theorize that they are "folded" into space-time. They're there, we just can't see them. As for whether this has any bearing on hyperspace, I have no idea.
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Sheridan: Are you trying to cheer me up?
Ivanova: No sir, wouldn't dream of it.
Sheridan: Good, I hate being cheered up. It's depressing.
Ivanova: So in that case we're all going to die horrible, painful, lingering deaths.
Sheridan: Thank you, I feel so much better now.