The double rainbow (secondary rainbow) forms when light undergoes two internal reflections inside raindrops (instead of one as in the primary). It appears about 9° above the primary, with inverted colours (red below, violet above).
It is fainter than the primary because each additional reflection loses light. The dark zone between both bows is called Alexander's band (after Alexander of Aphrodisias, 2nd century): it is darker than the surrounding sky because no light rays emerge at those angles. In exceptional conditions, third and fourth rainbows can be seen, but they are extremely rare.