The Super Game Boy let you play games that normally were about a quarter the size of an average postcard, and blow them up so that they were almost as big as a sheet of notebook paper. And, since they didn't take up all the room on your screen, you get these snazzy borders to take up the extra room. They don't really do much, though, other than just look kind of neat.
If you let them sit for long enough, though, stuff starts to happen. Little screen savery kinds of things. But, what if you want to see the screen savers without sitting there not touching the controller for several minutes at a time?
Easy. Just grab your controller, press L, L, R, R, L, L, L, L, R. You'll hear a 'ding' sound and the border's animation will start... assuming it has one.
A few of them, like the plain black border, don't do anything, though.