Strange button on my gear shifter?

My car is a 1998 Cadillac Catera. On the top of the gear shifter, which is located on the center console (by my right knee when I sit in the driver's seat), there is a circular button with an uppercase S on it. When I press it a warning light in the shape of a gear appears on my dashboard. My father originally thought it was a down shifting button,as that is the effect it seems to have when presses while the car is in motion, but I'm not completely sure. The car didn't come with a manual and they can be kinda pricey, so I can't just look it up either. If anyone could please give me some info. I would really appreciate it!!