There is a button next to the stick shift labelled Sport. It feels like it just re-maps the throttle so the pedal is more sensitive, but does it really change anything about the performance, suspension, or steering?
According to the Mini forums you'll get sharper throttle response. The throttle will seem to be respond quicker both opening and closing. The power steering effort will increase and on some models you get that racy exhaust noise while deaccellerating.