A color space is a mathematical transform on how a color is defined. This is similar to
coordinate space in
geometry (
cartesian,
radial, etc.). As with coordinate spaces in geometry, colors defined in one color space can be converted to another color space.
Color can be a tricky beast. In terms of light, red, green, and blue are the primary colors. This is why computers deal with RGB. In terms of pigments (ie paint), red, yellow, and blue are the primary colors. If you are working on a computer trying to produce a physical printed product, you will eventually need to convert the RGB pixels into something that can be printed.
Some of the common color spaces used include RGB (Red, Green, Blue), HSV (Hue, Saturation, Value), and CMYK (Cyan, Magenta, Yellow, blacK).
The benefits of different color spaces allows more efficient color computations for different tasks. Obviously, computers use an internal representation of RGB because light from the monitor produces the image. The HSV color space is useful for easily making a color lighter or darker without actually changing its hue. HSV can also easily change the hue while leaving the lightness or darkness intact.
CMYK color space is used for printing. If you ever read the color Sunday Comics in your favorite newspaper, you may notice the "color test dots" at the edge of the paper. There are four colors used to print the newpaper, and they are (surprise!) cyan, magenta, yellow, and black.
If this has perked your interest, you may want to fire up your favorite graphics program (like Fractal Painter, Photoshop, or the GIMP) and play around with the color selector. All of them allow you to choose different color spaces when selecting a color. Switch between the different color spaces and observe how each of them affect the way a color is produced. Its quite fun.