If you have a color printer, you know that the toner in the machine consists of these primary colors. Primary colors mean that all other colors can be created by mixing these colors together. Cyan, magenta and yellow are theoretically all you need, but to make a print look sharp and crisp you also use a black plate in the printing press. Naturally, red, green and blue are the primary colors in the RGB color space. It works with a fixed color value for each pixel.
Indexed files contain less data and therefore use less disk space.
If you are designing for the web, you'll have to consider that many computers can't display 24-bit color. There are a lot of people out there who are limited to 256 colors on their monitor. It may well come out looking bad, and it still takes as long to download. There are two kinds of image file formats you can use on the web - JPEG and GIF . There are advantages and disadvantages to both formats, and I'm not going to get into the big discussion about GIF vs. JPEG here.