The 11 dimensions predicted by string theory ( M-theory also) can sound like physics voodoo when you first hear about it, but it really isn't too hard to imagine as some physicist will have you believe. I will try and briefly explain where all of these extra dimensions come from...
We all know of the first 3 dimensions in space and the 4th through time (Yes classically the 4th dimension is time and not air being blown on to you like in a 4D experience ride). But where do the other 7 come from? Imagine some spheres, with there 3 dimension, all lined up together in the three dimension that you experience on a day to day basis. That is 3 sphere dimensions in each of the 3 classical dimensions, 3*3=9, giving 9 dimensions. But now you are thinking "A normal sphere has only three dimensions so no matter how many spheres you have it will still only be in three dimensions!?" Well yes this is 100% true. Mathematicians and physicist get around this by explaining these spheres' dimensions as "dimensions folded in on them selfs", so what we experience as 1 dimension is actually three!
The last 2 dimensions are easier; the first being time, which we all come across daily but yet is arguably the hardest to visualise. The second though is slightly easier to imagine though sounds very impressive. Curved space. When it comes to this dimension just try to think of the little spheres lining up in a way such that they are simply curved if you were to look at them from a great distance away. This means that what we would experience as travelling along straight line with all of our best instruments telling us so is actually not truly straight. Almost like walking in a seemingly flat straight line around the Earth would be curved because the Earth is round.
To sum up, 11 dimensions aren't as hard to imagine as you would first think. You have the first 9 with three dimensions folded in on them selves in the three dimensions that we experience every day. The 10th is curved space, or just those spheres lined up around a curvy bend. And finally the 11th is time which I am running out of.
