A secondary rainbow appears outside of a primary rainbow and develops when light entering a raindrop undergoes two internal reflections instead of just one (as is the case with a primary rainbow). The intensity of light is reduced even further by the second reflection, so secondary rainbows are not as bright as primary rainbows. Alternatively: fewer light rays go through the four-step sequence than the three-step sequence.
Photograph by: Olthoff
The color scheme of the secondary rainbow is opposite of the primary rainbow. Violet light from the higher drop enters the observer's eye, while red light from the same drop is incident elsewhere.
Simultaneously, red light from the lower drop enters the observer's eye and violet light is not seen. This is why the colors of a secondary rainbow change from violet on the top to red on the bottom.