From the Super Mario Wiki
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The Floating Jump (sometimes known as the Floaty Jump) is a move used by Princess Peach.
It first appears in Super Mario Bros. 2, where the player can hold the Jump button during a Jump to have Peach temporarily float a short horizontal distance. This ability was the result of Super Mario Bros. 2 being a repurposed version of Yume Kōjō: Doki Doki Panic, with Peach inheriting Lina's abilities, including her jump. The move returns in Super Smash Bros. Melee, Super Smash Bros. Brawl, Super Mario 3D World, Super Smash Bros. for Nintendo 3DS / Wii U, and Super Smash Bros. Ultimate with the same properties.
In Super Mario Run, the move works differently. Peach slowly descends mid-air instead of hovering.
In later games, such as Super Princess Peach, Yoshi's Island DS, and Super Paper Mario, Peach can use her parasol to float. She also uses her parasol as her up special in the Super Smash Bros. series. In Super Smash Bros. Ultimate, this move, as well as the parasol, is also present for Daisy, and works in the same fashion as Peach's, due to her being an Echo Fighter of Peach.
It also appears in Mini Mario & Friends: amiibo Challenge, where it appears as Mini Peach's special move. It is performed whenever the toy walks off a platform or a ledge, making her capable of floating across large gaps. This grants Mini Peach access to areas other Minis cannot reach. The move needs to be executed in Level 6 to access Mini Peach's assigned amiibo Door by removing a Long Spring that leads to it. The door leads to Mini Peach's set of levels, Balloon Float Castle, where she makes extensive use of this ability.