Stone Mania

Chatoyancy or chatoyance, is an optical reflectance seen in certain .  Good quality Tigers Eye is just one which is particularly well known for being chatoyant.

Originating from the French word for 'cat's eye', the effect is caused because of either the fibrous structure of a material or the fibrous inclusions or cavities within a gemstone.  The effect can best be seen when a gemstone is moved in the light and can possibly be compared to looking at a highly polished spool of silk.  It many cases it will appear as if the patterns or markings are actually moving around.

Chatoyancy is most often seen in gemstones which have not been faceted.

Further reading:
Chatoyancy