The Banana Peel can be thrown like any other regular item, and when a character other than its thrower steps on it they slip and are temporarily stunned. The banana itself flies a short distance sideways, just far enough that if the slipper rolls the wrong way, they will slip again. Diddy Kong's down special move generates Banana Peels even with items turned off, which is an important strategy in tournaments because it often disrupts an opponent's ground game, forcing them into the air. Banana Peels can also make opponents trip if their feet or shins touch a stationary banana during an attack on a platform above them.
Bananas retain the same functionality in Smash 4, with one critical difference - as soon as any character slips on them, they disappear, so they cannot be used more than once. This change did not exist in early versions of Smash 4.
In-game description from Super Smash Bros. for Nintendo 3DS
A classic comedy staple: step on one of these and you'll fall on your rump. It never gets old!
The peel from a Japanese fiber banana of the Musaceae plant family. It contains a high volume of vegetable oil, which oozes out when the peel is stepped on, making things slippery. In Smash Bros., the peel fulfils its destiny as a comedic prop by making passersby slip. Characters who land on their backsides will be defenseless until they recover their footing.
Looks like someone had a nice snack and didn't bother to clean up afterward... As you may suspect, stepping on a banana peel sends you falling to the ground and exposes you to attacks. You can throw these at your opponents too, but please clean up when you're done, all right?
HEY! Put that banana peel in the bin! ...Oh, you're going to trip up your opponent with it? Carry on, then. Of course, picking up and throwing banana peels at people is disgusting, but they'll have a hard time keeping their defences up if they're putting on a one-man slapstick act, so...go ahead.
This item made its first appearance in Super Mario Kart. In said game, the banana peel is an item that the player can throw on the road. If that same player or other players hit the banana peel, their kart will slip and spin around. The banana peel has appeared in every Mario Kart game since. In Brawl, the banana peel can be picked up and thrown on the floor. If a person moves over the banana peel, the person will trip; however, the banana peel does not work on the person who threw it.
While depicted as having faces in the Mario Kart series, the Banana Peels in Smash lack these faces.