Floating refers to a technique that only Peach can perform in both Super Smash Bros. Melee and Super Smash Bros. Brawl if the player holds the jump button or taps the control stick up and holds it. While Peach is in the air, she will float for several seconds (in Brawl, 2.5 seconds). Peach can move horizontally while floating but will not move vertically. The player can also press the attack button while floating to perform an aerial atack, which will still keep Peach floating after the duration of the attack is finished. The float is a major part of Peach's recovery and frequently is used in competitive play, especially due to auto-floating and float canceling.
In order to float on command — and at any height — the player must jump and press down when at the desired height while holding the jump button. Once the player has hit down while holding the jump button, they can hold up and let go of the jump button and keep on floating. This technique has been dubbed the "auto-float" by SuperDoodleMan. Floating at different heights has varying uses depending upon which height the player chooses, but they will generally find themselves floating either at short hop height or just above the ground. If they are falling down, and they have yet to use their float, they can press down and the jump button simultaneously, but make absolutely sure to do so at the same time; otherwise, they will waste their double jump and just float, which could prove disastrous while being edgeguarded. A double blue circle from a double jump or the very distinct sound effect of her double jump will give the player a notice that the technique has been performed successfully.
Float canceling (or FCing) is a Melee-exclusive bug relating to floating. If Peach uses an aerial attack while floating, landing during the attack (whether still floating or not) will skip landing lag entirely and result in a normal landing instead. Float canceling is more potent at lag reduction than L-canceling (which can only halve landing lag, not completely skip it) and is significantly easier to perform, making the technique essential above low levels of play.
Using float canceling to generate effectively lagless aerials is arguably the most important aspect of Peach's one-on-one combat, as it allows her to combo from almost any aerial at low percents (and some such as down aerial at higher percents) and makes it significantly more difficult to shield grab her from the air. In combination with ground-level auto-floating, Peach can jump, use an aerial, and land ready to do something else faster than any other character.
Some uses of ground floating include, but are not explicitly limited to:
At her full jump height, the player can abuse the benefits of Peach's aerial arsenal, especially the spacing on her forward aerial and down aerial. Peach's full jump height can also be used to punish overaggressive combatants or overzealous players who like to jump the gun and attack too early. For example, a player who is using Falco and constantly firing off SHLs, or a player busy SHFFL'ing, can be punished with a float canceled aerial. Ground floating should be used against opponents who remain airborne; it may also be used for following an opponent's DI from one of her launcher attacks.
Peach's float ability originates from Super Mario Bros. 2 in which she was the only playable character to be able to float. Super Mario Bros. 2 was itself based on a game called Doki Doki Panic. In this game, the character Lina had the ability to float, and she was replaced by Peach in the Mario-themed port.