Rainbows are created when sunlight enters a raindrop, bends, reflects off the inside of the drop, and bends again as it exits. Different colors leave at slightly different angles, which is why you see a band of separated color instead of plain white light.
That is also why rainbows show up when the Sun is behind you and rain is in front of you. You are seeing lots of tiny water droplets doing the same light trick at once.
The result looks magical, but the mechanism is straightforward optics. Sunlight plus droplets plus the right angle equals the arc people recognize instantly.
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