Two ways: First, in air conditioned environments, reducing humidity will make the air more comfortable and will feel a little cooler. (EPA recommend 30% – 60% indoor humidity levels.) This will allow your thermostat to be raised a few degrees.
Utility companies say that you can save about 5% for every degree you can increase the thermostat. Secondly, by reducing moisture in any refrigerated or air conditioned environment, you are reducing “latent heat”. This latent load is additional heat your system must remove in order to cool. By reducing the latent heat load the system will run more efficiently and will use less energy. This is not theory, but a proven fact.