Why is white light not just a single colour?

The fact that white light can be split into multiple colours by a prism or a load of raindrops to form a rainbow shows it is not a single colour. It also looks white because the receptor cells in our eyes ( the cones or colour sensitive cells ) tell our brains it just looks that way!

We see colours based on the mix of wavelengths of light absorbed by the cone cells in our eyes. As we have three types (roughly speaking red, green and blue) every colour we perceive can be mimicked by using combinations of those three colours (i.e. wavelengths) of light. White is what we see when we have an equal amount of light hitting each type of cone, but that can only happen if there is a mixture of wavelengths, so white light has to be made of a mix of colours.