When you think about the vast array of lights and lighting tools that are used on a film set, it seems ridiculous to be talking about simplicity, but it really is the key to great images. 90% of those lighting instruments sit idly by during any given scene, with just a few actually in use. Amateur videographers often approach a scene asking, "is there anywhere that needs more light?" Experienced DP's realize that shadow areas are just as critical to the image as lit areas. By using fewer lights, and flagging those off properly, you can create an artistic and more dramatic look to your scene. It is the difference between the wash-lighting look of a sitcom, and the sculptured look of a big-budget motion picture.
Another important reason to simplify is that you eliminate multiple shadows. Nothing is more unnatural than shadows being cast in three different directions by a single object. Using bounce techniques instead of additional lights is a good way to minimize this problem. And finally, using less light allows the camera iris to be opened wider for a shallower depth of field. While it is possible to stop down using neutral density filters, the less glass you have to put in front of the lens, the better.