In Chapter 6, Typography, we discussed the idea of web-safe fonts and how the Web has moved on a little bit from there. The concept of web-safe colors is also going the way of the dodo and is not really a consideration unless you know your target audience is using ancient monitors that can only display 256 colors.
Just to give a very brief history lesson, web-safe colors were a small palette of fewer than 256 colors that would display properly on both Windows computer and Mac computer monitors. Today's monitors can show literally millions of colors; even the phone in your pocket can handle more colors today than those old monitors.
If you're using Photoshop or Illustrator to create your graphics, you'll see that when you choose Save for Web & Devices, you can still convert the colors in your image to their web-safe equivalent by using the Color Table section. You can also see the web-safe color palette by using the context-sensitive menu on the Swatches...