The idea of a multi-dimensional universe is heavily based on mathematical theories. Using advanced mathematics it is very easy to model 4, 5, 200 dimensional spaces, although is it unconceivable to human beings to perceive any dimension other than the four ones aforementioned by Sydney. We can't even perceive Time as a fourth dimension of our space.
If you get the right knowledge, and some free time, you can try to imagine Time as another dimenion of a 4D space, and even see how objects move within this space.
Some guys at my college, students of Physics, said they did that once, but that would cost a whole night awake to accomplish such a difficult brain task (those guys are nuts, thats what they are).
Using plain algebra and vectorial calculus, is is possible to create multi dimensional spaces in theory, spaces that doesn't deny any of our known physics laws. It doesnt mean they really exist in our universe, though.
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