Running shoes are designed to absorb energy, to make them comfortable and protect your feet. To do this they have to be soft and squishy, but if you walked on a soft material it would flatten out, getting deader and deader as you went through the day. To stop this, we need to add hard bits to the formulation. These prevent the shape squishing too far, and allow it to rebound after each step. As a result, the running shoe stays in shape. The nanotechnology comes in because the soft and the hard bits we use are the size of polymer molecules.