If you mean "dimensions" in the sense commonly used by mathematicians and physicists, these are a human concept, invented to simplify mathematical descriptions of the physical world.
- Dex, Karen and presumably Cecil of The Straight Dope (www.straightdope.com).
That is way better than the four times and ten ways I tried to put it!
"All of space has three dimensions; time does not exist. / As we approach the speed of light, the clock remembers this"
Now that quote is by no means The Straight Dope. And is Cecil really an intellectually self-deprecating heterosexual or what? "The Straight Dope?" What's he trying to tell us there.
But in any case, for the record: and purely for conceptual purposes, the best humans at it calculate reality along twelve dimensions. Nine of space, and two of time. Four extended and perceptible at our scale of observation, all the rest curled up tinier than our highest-resolution devices can measure or perceive, metaphorically at least you might say they were curled up so tight they were approximately the size of quanta. But put 'em all together, three of space and one of time all unfurled, plus seven more of space and one more of time all curled, they could go like so:
1. height
2. width
3. depth
4. time
5. space (curled up)
6. space (curled up)
7. space (curled up)
8. time (curled up)
9. space (curled up)
10. space (curled up)
11. space (curled up)
12. magic (no I'm kidding, it's more space curled up)
As you can see, humanity has never bothered to name the curled-up ones, because they aren't perceptible to us. There's no social or cultural reason to name them. At no point are you ever going to be leaning back eyeing some girl's behind which happens to be extra-well endowed in the 10th dimension for some reason, and remark, "Wow, check out the zidth on THAT! HOWZA!!" It'll never happen. Imperceptible dimensions add nothing to our experience.
I'm mostly only putting this numbered list here because...embarrassingly enough, I keep forgetting how many curled-up dimensions there really are. Can you believe it? "How many dimensions total again? Ten or eleven," I'll ask - like I'm going to get that answer right! Try twelve, jackass. Because it's twelve.
Anyway, now I'll have one easy place to look next time I need to know. But if you're asking yourself, "well that's well and good for him, but what do these extra dimensions mean to me?," well, to return again to the Straight Dope, the chief point to remember is -
"So what we're telling you is, there's nothing magical or mysterious about dimensions. They're just notions scientists dreamed up to help them describe the world."
— Dex
Quite so, Dex. You go, motherson. Couldn't have said it simpler m'self, and I should know, having tried.
Footnote.
http://www.straightdope.com/columns/read/1655/how-many-dimensions-are-there-and-what-are-they
All further references within text.