Modern physics has good theories for quantum mechanics, relativity,
and gravity. But these theories do not quite work with each other.
There are problems caused by our living in three spatial dimensions.
If we lived in more than three dimensions, these problems would
naturally resolve themselves.
String Theory, one of the recent proposals of modern physics,
suggests that in a world with three ordinary dimensions and
some additional very "small" dimensions, particles are
strings and membranes. Yes, membranes in extra dimensions are weird
and hard to visualize. And what are "small dimensions?"