Rainbows are created when there are water droplets (mist or rain) in the air AND the sun is shining. Sunlight enters the water droplet and, because of the droplet's spherical shape, the light is bent (refraction). When sunlight hits a water droplet at just the right angle, the light is separated into different color and we see a rainbow.

Here's a good website for you to check out:
rainbow

Rain forms when water vapor condenses (turns to liquid water) around some nucleus (like a dust particle) and the water droplet gets heavy enough to fall to the ground.