Our eyes and brains see different frequencies of light as different colours, from red, through green, to blue. The raindrop in a rainbow splits the colours up and orders them according to frequency, and thats how we happen to see those colours.
All of the colours of the rainbow make up visible light and like Ian has mentioned, they are of different frequencies, or wavelengths which bend differently when you shine light through a prism.
When it rains, water droplets act like a prism, refracting light from the sun. When light is bent, its speed slows down and longer wavelengths like red slow down the most, causing it to be refracted the most and causing violet to be refracted the least – this is why you see the colours in that order.
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