A rainbow is created when light and enough water vapor in the atmosphere interact with each other. The position of the observer is also important. The sun must be behind you, the water vapor in the air must be in front of you, and the clouds need to be cleared away.
Let's talk about the nature of light in order to better understand rainbows. Light is an electromagnetic wave, and white light is actually comprised of many colors. Specifically, white light is made of red, orange, yellow, green, blue, indigo, and violet light. When light moves from one medium to the next, it bends. This particular wave interaction is called refraction. Because light is made of different colors (each with its own wavelength and frequency), each color bends a little bit differently than the other colors. Violet bends the most, and red bends the least. When white light is refracted, the individual light colors are spread apart and become visible.
So how does this apply to rainbows? As sunlight streams into air that has a lot of water vapor, the white light is refracted (bent) by the denser water droplets. It then reflects off of the back of the water droplet, exits the water droplet, and gets refracted one more time. This is the light that eventually reaches your eyes, and you see the entire color spectrum as a rainbow.
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