The Sport Mode offers you the grace of God!!!
Really though.... the sport mode activates different mapping for the throttle.
Since the S54 engine (2001-2002 M-Coupe/Roadster + 2001-2004 M3) has servo controlled throttles (meaning it's not mechanically operated via cable) the computer can essentially adjust the sensitivity of the throttle.
What it bears down to is the amount of pedal travel necessary to open the throttles. Sport mode is direct response (think of an aspect ratio of 1:1) where normal mode is delayed (1.2:1 - or something similar).
Raaaappp rRAAAAAAAAApppp Shhhsttt...