From the Super Mario Wiki
The Stretch Punch is an extendable boxing glove. Upon using the Stretch Punch, the user will begin to repeatedly extend it for approximately 5 seconds. If a rival gets too close to the attacking racer, the rival will get hit and be brought to a complete stop.
A variant of the Stretch Punch known as the Stretch Punch+ exists exclusively in Mario Kart Arcade GP. This variant extends the duration of the attack by around 2 seconds.
The Stretch Punch is the only close-range melee item that has a unique character animation when in use - all other melee items reuse the swinging animation of the Thunder Stick. In addition, the Stretch Punch is one of two melee items to have a unique sound when in use - it plays a spring sound every time it is extended. The other item is the Quack Hammer.