This has a profound implication. It basically says that gravity permeates three-dimensional space, but no higher dimension, perceived or otherwise. The reason is similar to why the brightness of a light bulb diminishes as the inverse square of the distance from it. The light spreads out over an ever larger surface. In a three-dimensional world, surfaces have two dimensions, and the light is diluted by the size of the surface it must fill, hence by distance squared.
Gravity works is a similar way.
Gravity does not work that way, hence no higher dimension. Now, this argument is under severe and excited assault . The new perspectives have emerged from work on String theory and the mathematically constrained result that there must be 10 or 11 spatial dimensions to make a self-consistent theory. Randall and Sundrum realized that, mathematically at least, that need not be so. More complicated couplings could exist that are completely consistent with the mathematics of Einstein's theory and of String theory.