From back of box:
Bring the professional feel of a real arcade joy stick out of the arcades and into your livingroom. With NES Advantage the action never stops. Just a touch of a button and you'll have adjustable, repeat firing power at your fingertips. And when the action gets too fast, you can slow it down with the exclusive slow motion control that allows you time to plan your next move. Play it alone, or flip the switch to two players, so you and a friend can get the NES Advantage on most games. The NES Advantage. For use only with the Nintendo Entertainment System.

That says most of it! Released in 1988, this sucker was awesome! The buttons were huge and the entire thing was very durable. The slow motion was simply a rapid pause/unpause and didn't work for games like Zelda where the pausing brings up an inventory or game settings menu. One of the most famous uses of the Advantage was in Ghostbusters II when it was plugged into the Statue of Liberty to bring good feelings to all of the people of New York City.
You can get a used Advantage from for US$4.95