There are two models of colors: additive and subtractive. Additive color is what happens with light: if you mix red and green, you get yellow. If you mix red and blue, you get cyan. If you mix everything, you get white. Subtractive color is what happens with inks, pigments, and dyes: if you mix red and green, you get brown, and if you mix everything, you get black. CRTs and LCDs use additive color models because they’re working with light; printers use subtractive color models because they’re working with inks.
The “white” is a diffused flourescent (or lately, LED) lamp behind a layer of tiny liquid crystal “shutters” with color filters on them. Open all the shutters, and you get white light. See this for details.
LCD and CRT displays are made up of pixels (the unit of measurement when you hear 1024×768, for example). Each pixel is made up of three, teeny, tiny dots (sub-pixels), one each for red, green, and blue (have you heard of RGB?). When all three sub-pixels are illuminated at full brightness, you get white. When all are fully off, you get black. Every other colour is made by combining different brightnesses of R, G, and B.