Can be seen best in colourless Diamonds, Zircon and also Sphene.
White light that we see all around us, from either the sun or indoor lighting, is actually made up of different colours, all of which have different wavelengths. Each of these wavelengths as they pass from air into a denser material, such as glass, bend (refract) at different angles. When denser material such as a gemstone (or a glass prism like those used in schools) demonstrates this effect, the light bounces off its inclined surfaces and the split becomes visible to the eye.
Not all gems demonstrate dispersion, and it is dependent on their refractive index and their density, plus of course how well the gem is cut.
Zircon and Diamond are two of the most well-known gems that offer beautiful dispersion, but the top of the class is the lesser-known gemstone Sphene. Other names often used to describe dispersion are fire and scintillation. However scintillation should really only be used to describe the surface lustre of a gemstone.
Diamonds that show the best dispersion are those that are colourless. The best way to understand this is to imagine how tinted glass acts as a filter, through which very few colours are seen. Therefore gemstones that are colourless will tend to have greater dispersion.