Rather than have to pull the line off the carb of off a fuel filter every time you want to fill up, you either use a "t" in the fuel line or a third, dedicated line to fill the airplane. The fuel dot is used to plug the end of the line. If you have a cowled airplane, the outer part of teh dot is mounted into your cowl, and the inner part of the dot, that actually plugs the fuel line, is pressed into place inside it. It holds it securely, and is a lot neater than having a fuel line dangling out the bottom of your airplane.

This is the best pic I have of a fuel dot. This is the Du-Bro setup. The center pulls out, with the fuel hose plugged into the rear of it. The outer part stays with the cowl. Very neat install.