So-called stainless steels contain chromium (and usually nickel) in the alloy. Chromium oxide forms on the surface and forms a hard passivation layer (similar to the aluminum oxide layer that forms naturally on aluminum).
Originally Posted by TheFlyingCamera
One should never use steel wool (or steel wool scouring pads such as Brillo) on stainless steel. Fine iron particles from the steel wool can get under the abraded-off chromium oxide surface passivation and then rust.
If you need to scrub stainless steel with an abrasive, use ScotchBrite or similar non-metallic pads.
Non-scratch cleansers such as BonAmi can work on less-difficult stains on stainless steel.