First described by James Clark Maxwell in the mid 1800s, the color additive theory describes how we perceive color and how they are created. Essentially white light is a combination of many different colors, a continuum of wavelengths organized into "bands" which we label with names (blue, green, red etc). When equal parts of each of the three major bands are combined you get white light. White light is the sum of red, green and blue. This is additive color.
Red, green and blue are the "primary" colors of white light. All three colors will result in white, the absence of all three will produce black.
When two primary colors of light are added together, you get a color that is brighter than either of its components.
These are the "additive" combinations:
By using unequal amounts of red, green and blue light you can create new colors. Using red, green and blue, the entire spectrum of visible light can be created.
A TV monitor uses additive color. Three beams of electrons corresponding to red, blue and green are projected onto a fluorescent screen. The pixels of the screen are made of triads which are sensitive to the three colors, based on the proportion of red, blue or green light striking the triad the pixel can appear in any single color.
Printing a color image on a piece of paper uses the "subtractive" colors (cyan, magenta and yellow) to produce red, blue and green.