A rainbow is an optical illusion; it isn't really there. The observer of a rainbow is seeing sunlight that has been reflected and refracted — separated into its visible colors — by raindrops. A rainbow forms when it is raining opposite the sun and you are in between the sun and the raindrops. One can never get to the spot where the rainbow ends because the rainbow image moves with the observer.
A double rainbow happens when the sunlight is reaching your eyes is less impeded, and so you can also see the secondary reflection. The colors of the second rainbow are in the opposite order of the primary rainbow. The full rainbow, if you could see it, is a complete circle. You can never have a rainbow at noon because it would be below the ground. If a rainbow seems particularly flat and low to the ground, it is because the sun is still high in the sky and you are seeing just the top part of the rainbow.