I have heard that there are 12 spatial dimensions. Does this mean that this many are possible, or that 12 dimensions actually exist? If the latter, then do the same things that exist in 3 dimensions exist in 4 or 5 dimensions as well? Or are the other dimensions a whole new world, like an alternate universe? I'm confused!
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An informal answer until you get one from an expert: the extra spatial dimensions are spatial dimensions conceptually similar to the ones in our 3D space, and the objects exists in this higher dimensional space. The reason you do not notice them macroscopically (such as why an object cannot change direction into the fourth spatial dimension and disappear from your view is that these extra dimensions are assumed to be curled into very small loops, so their effect will be only observed for particles small enough to be able to actually move or interact into those extra dimensions (of course, this is just one of the current theories, there might be no extra dimensions at all).