When every day begins with a "why" question and ends with another "why" question, it's inevitable that your little scientist will ask how rainbows are formed. From your child's point of view, they just magically appear after it rains. Just in case explanations of fairies and leprechauns don't work for your child, you can explain how that beautiful smudge of color in the sky formed. It all centers around the refraction of light.
Ask your child when rainbows appear. Does she know they only appear after rain? Explain that not all the water falls down to the ground and that there's still water in the air after it rains, making it feel moist.
Help your child remember a time when she's seen mist or fog. Explain that the air around where a rainbow forms has a lot of water in it, just like the fog she saw by grandma and grandpa's farm. She might not be able to see the drops as clearly because they're small, but they are there.
Explain that light refracts when it hits the water, making colors. This is the tricky part. Try putting a glass of water on a sunny window ledge or even in front of a lamp. Show her how the reflection of the light on the other side of the glass doesn't look like the lamp because it spreads out into odd shapes.
Explain that all sunlight has all the colors of the rainbow in it but you can't see those colors. Rainbows are an exception. Another way to show this, and easier to do than find a rainbow, is to use a mirror to reflect sunlight onto a wall. When you find the right angle, you'll make stripes of color.
Supervise your child while she plays with a mirror to make her own rainbows. Show her how if you tilt the mirror in a certain direction, it still reflects light but will not make a rainbow. Rainbows can only be seen under the right conditions and from the right angle.