A moonbow is just like a rainbow except it is produced by a strong moonlight. The colors tend to be more faint because there is less light hitting the water droplets.
Moonbows are rare because moonlight is not very bright. A bright moon near to full is needed, it must be raining opposite the moon, the sky must be dark and the moon must be less than 42º high. Put all these together and you do not get to see a moonbow very often! To the unaided eye they usually appear, as in the thumbnail, without colour because their light is not bright enough to activate the cone colour receptors in our eyes. Nonetheless colours have been reported and might be seen when the moon is bright.
Image shot on oct 08 at 10;20 PM with a Nikon D70 @ 1600 ASA - 22 seconds exposure and no post-processing.