A dimension as such is very difficult to conceptualize or visualize, apart from the space-time dimension. A clearer understanding of it can be got from the knowledge of higher mathematics. If you consider a room to be a dimension (other than space-time), the space comprising of that dimension is curled to such a great extent that if you walk through a wall on the left, you immediately come back into the room through the right wall. If you consider this room shrunken into a very small size that compacts entity is a dimension. Well, the explanation may not sound satisfactory, but a bit of research on string theory may yield better answers. But till now all the other dimensions are understood mathematically only.
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