|MadSci Network: Astronomy|
First of all, you're lucky to have seen this! The answer is that the Moonbow is caused by exactly the same mechanism as a normal rainbow; light passing through water droplets is split into its constitent colours which is what we see as a rainbow. The only difference is that here the light is from the Moon rather than the Sun. We see the whole circle however unlike the Sun where the horizon gets in the way. Normally moonbows appear white, because the light is fainter and the eye isn't very good at picking out colour in low light. When conditions are perfect, however, you can just get lucky!
Try the links in the MadSci Library for more information on Astronomy.