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Unfortunately you are not going to understand the arguments for multi-deminsional universes (at least not by reading books such as . You might be able to grasp the general ideas (where books like "The Elegant Universe" and "A Brief History of Time" shine) , but the basis for most multi-dimensional theories are on advanced mathmatics. The reason 11 (I think that is the current prefered amount of dimensions) is favored is that is what works with some of the math. Unfortunately, the math is so complex and the ideas so hard to wrap ones brain around, that scientists studying this have really only begun to scratch the service and without a major breakthrough will likely keep scratching away... We need a new Einstein to explain this all to us.
Which brings me to the more accepted and slightly easier to understand concept of the "Fourth Dimension", time. The pictures and ideas like the Klein bottle are purely dealing with four spacial dimensions. Time is its own unique dimension, though there is no reason to rule out there being two or more time dimensions, most theories favor there being only one. Maybe because the idea of multiple time dimensions is even harder to understand than more than three spacial dimensions. Where time gets wrapped up into the dimension business is with Einstein's Relativity. For example, the equations state that if you move in one dimension, either three spacial dimensions or the one time dimension, you move slower in the others. Therefore if you travel the speed of light (the fastest anything can move according to relativity) in one direction you will not be moving through time at all...
Well, that is the way I remember it anyway...
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