Light traveling through raindrops is reflected once to form a single rainbow and twice to form a double rainbow! The double reflection within the drop causes the light to exit at a greater angle. This affect produces the second rainbow composed of reversed colors!
See how the primary rainbow is ROYGBIV and the secondary rainbow is VIBGYOR?
Here are some GreenAnswers questions dealing with simultaneous rainbows. The first link offers an even more detailed description of the cause than letusgambol has given (which is a good explanation):
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