Diamond has a higher index of refraction than ordinary glass, and is also more "dispersive". The index of refraction of diamond varies more with the wavelength of the light than does that of glass. This makes diamonds spread the colors of light through larger angles if it is cut in a shape of a prism, or in fancy, expensively-cut diamonds, into a large array of angled surfaces. The high index of refraction also increases the amount of light which bounces internally off of a cut surface ...the buzzword here is "total internal reflection". These properties make cut diamonds look brighter and more colorful than a similarly cut piece of glass.