Dimension in physics

I have a solid understanding of topological dimension. I heard that some string theororists think that the universe is >= 10-dimensional, but that the extra 7+ dimensions are too small for us to encounter. How can a dimension be small; is it just a model for what is observed, or is it based in theory?

small as in it is of length ~ 2pi h and compact (i.e. S^1). think of a really tiny circle.