Most of these answers are wrong...

Sport mode basically makes the gas pedal LESS linear. The gas pedal feels more sensitive because nearly all throttle input is moved to the front of the pedal hence why the car feels more powerful in light driving.

It begs to be mashed on, and is unsafe when driving hard. The car is not more powerful in sport mode. 100% throttle with the sport button on/off is the same as 100% throttle to the engine.

Pointless button IMO because it just makes you FEEL faster. Plain and simple.