The simplest string theories pertain to a universe with 9 spatial dimensions. Since we only perceive 3 spatial dimensions, string theorists suggest that the additional dimensions curl in on themselves and are very small. There are at least hundreds of thousands of geometrically and topologically distinct forms that 6 compactified dimensions could take. This adds to the proliferation of string theories that could correspond to our universe.

The extra dimensions may or may not have any real existence. They could just be a theoretical device. But regardless of their ontological status, the properties of any extra dimensions would influence the physics of our universe.

Although string theories describe the motions of continuous strings in a continuous background spacetime, they seem to suggest that spacetime is discrete. This is apparent in a spacetime with one dimension that is curled up into the topological equivalent of a circle, as I have drawn above. In this case, the vibrational modes of strings wrapped around a compact dimension with a diameter larger than a critical diameter are equivalent to the vibrational modes of strings wrapped a larger number of times around a compact dimension with diameter smaller than the critical value. So there is essentially a smallest diameter for the compactified dimension, i.e. a discretization of the compact dimension.

String theories also alter the uncertainty principle by adding a term to the inequality. Notice that this term involves a constant designated by a capitol C, which is not the same as the speed of light in a vacuum. Under the form appropriate for string theories, there is a minimum possible uncertainty in the position, which corresponds to a minimum resolution for any spatial measurement and a de facto discretization of space. I have written the minimum value for the uncertainty in position above.