String Theory predicts the existence of more than the 3 space dimensions and 1 time dimension we are all familiar with. According to string theory, there are additional dimensions that we are unfamiliar with because they are curled up into tiny complicated shapes that can only be seen on tiny scales. If we could shrink to this tiny, Planck-sized scale we could see that at every 3D point in space, we can also explore 6 additional dimensions. This animation shows a Calabi-Yau surface which is a projection of these higher dimensions into the more familiar dimensions we are aware of.
Brian Greene’s book, The Elegant Universe, was made into a documentary and has a chapter that does a good job of explaining this concept. The Elegant Universe [documentary]