Colour-blindness happens if people have problems with the colour receptors on the retina, at the back of their eyes. It can be a genetic problem, or in some cases as a result of degenerative eye diseases. Humans have three different types of colour receptors (called cones), which are sensitive to different portions of the colour spectrum. Basically, you see colour because your brain compares the responses of two different cones, and that gives it an idea as to what part of the colour spectrum it’s from. With colour-blindness, if you lose one (or two) of these cone types, then you can’t make those comparisons, and so your ability to make fine distinctions about precisely which part of the colour spectrum the light is in is lost.
Think of it like one of those water taps that mixes both hot and cold water. If you have only the hot water tap, all you can do is change how much water is coming out of the tap (how intense the colour is), but the water will always be hot (one colour). If you add a second, cold tap, not only can you change the amount of water coming out, but you can now change the temperature in a much more varied way.