Web safe colors are the colors that Netscape
picked to be the standard palette
if the computer could only display 256 colors. This way, artists that were making graphics could be guaranteed that specific colors would exist.
The "ideal" color space on a computer is 24-bits. One byte for each red, green, and blue. This yields a possiblity of 16.7 million colors. This is way beyond the 256 colors that some computers have as their maximum. So, Netscape gave each red, green, and blue 6 values to choose from:
0, 51, 102, 153, 204, 255 (00,33,66,99,CC, and FF in hex)
Each color consists of a red, green, and blue value. So an example of a valid "web safe" color would be "CC00CC" (a medium purple), or "FF0000" (pure red), or "CCCC99" (an olive color).
This gives a 6x6x6 color space consisting of 216 colors. In Netscape, it is guaranteed that if you use these colors they will always be displayed correctly. If you use a color that is not "web safe", it may be significantly different on 256 color displays (and possibly incorrect in 16-bit displays also, but thats another discussion...).