From the Super Mario Wiki
A Parasol is an item from the Kirby series. It appears in Super Smash Bros. Melee. Players can use it to hit other players, and can do quite a bit of damage if used correctly. The Parasol also slows down the player holding it when he or she is falling. To stop floating while in mid-flight, the player has to tilt down on the control stick. If Peach uses the Peach Parasol move while holding this item, she will subsequently replace her usual Parasol with this Parasol. There is a similar item called the Bumperchute from Yoshi's Story.
The Parasol, which was originally used by Kirby, can be used as a weapon to bludgeon enemies. Even better is that fact that players can open it while airborne and lazily float back toward safe ground. It's incredibly useful in returning to the field of play after an opponent gets the better of you and sends you flying.