What gives clouds their colour?

Color is an interesting thing. What we think of as white light is actually made up of all the colors of light mixed together. This is what you are seeing when you view a rainbow. The water drops have split the sunlight apart into the full spectrum. Consider that when you see anything, light is reflecting off that object and entering your eye. Things appear to be certain colors because they absorb some colors and reflect others. A shirt that we see as blue is reflecting the blue light and absorbing the reds and yellows.

So, as light comes through clouds and reflects off clouds some colors are absorbed and others are reflected. It depends mostly on how much liquid they contain; how dense they are. It can also be affected by the clouds temperature.