Moonstone is a variety of feldspar and the shimmer, which is called schiller or adularescence, is caused by the intergrowth of two different types of feldspar (orthoclase and albite), with different refractive indexes.
That's the science bit now for the legend!
The Romans thought that moonstone was formed out of moonlight and to this day in India it is considered a sacred stone.
Moonstones come in a variety of colours. The body colour can range from colourless to grey, brown, yellow, green, or pink. The clarity ranges from transparent to translucent. The best moonstone has a blue sheen, perfect clarity, and a colourless body colour.