The color of light is determined by its wavelength. Red has the longest wavelength, continuing through the colors of the rainbow (ROY G BIV). This is a continuous spectrum with no real distinctions between any given shades.
Light that appears white to us is an even mixture of all the wavelengths.
'Black' simply is an absence of any light at all.
In the attached picture, you can see how monitors and other things create a fair approximation of the full spectrum of colors by mixing red, green, and blue together in various amounts.
LeisureLife's response is on the right track but somewhat backwards. It can seem this way when dealing with paints because of the way they work. As opposed to monitors which create light, pigments and dyes work by absorbing it.
For example, yellow paint looks yellow because it absorbs everything but the yellow wavelengths (which it reflects back out) from the full spectrum of white light in the room. So, combining red, yellow, and blue paint in his example will overlap and end up absorbing some of every wavelength. This again gives an absence of light which appears black.