Gemologist, Wink Jones, an online diamond retailer explains how the shape of a diamond cut affects the quality of the cut. Typically when people talk about cut they actually mean shape of the diamond cut. Shapes of diamond cuts are princess, round, oval, marquise, etc. But quality of the cut has to do much more with how the diamond sparkles than the actual shape.
Video Link: http://www.youtube.com/watch?v=2PlUgV2FB_Y