Pleochroism is an optical phenomenon that's seen in certain minerals and gemstones. It gives the impression that a stone is a different colour depending on the angle at which it's viewed. The change in colour is caused by the material's ability to adsorb different wavelengths of transmitted light depending on the angle of the crystal.
Pleochroism is useful in order to identify certain minerals and gemstones because the colours that can be seen from different angles can help with identification of its crystalline structure. Stones which may appear to be very similar often have different pleochroic colour schemes.
As an example amethyst exhibits pleochroism although it's not particularly strong. Depending on the light that's present the purple colour of the quartz can appear to be different. Other examples include the minerals beryl, corundum, topaz and tanzanite to name just a few and the colour of a mineral or gemstone that exhibits pleochroism can affect the strength of the optical phenomenon.