When he uses Fire Fox, Fox charges the move while being surrounded by flames (Super Smash Bros. Melee onward), and then he flies in the direction inputted on the control stick or d-pad. The move has a fire effect throughout the entire move. Falco and Wolf have similar moves, Fire Bird and Fire Wolf, respectively (although Wolf's version does not actually involve fire, despite its name).
Fire Fox is Fox's primary vertical recovery move. The attack can deal around 28% damage, provided the opponent is hit by both the charge-up and recovery. Fire Fox, out of all the Star Fox characters' recoveries, covers the greatest distance. However, unlike Wolf and Falco's versions, Fox's Fire Fox only hits opponents once, not having many multiple hits during charge-up or after being executed. It is highly likely to return to the ledge of the stage by using Fire Fox to recover, due to its long traveling distance. Additionally, if Fox hits the ground before the attack ends, Fox will slide on the ground in a wavedash-like manner, cancelling any endlag from the attack.
In the original Super Smash Bros. for the Nintendo 64, Fire Fox was notably different from Super Smash Bros. Melee and Super Smash Bros. Brawl. Fox charges the move with a large flame-shaped aura (and was pulled down by gravity at a reduced rate), and then propelled himself with an explosion, similar to PK Thunder 2. The charging does not inflict damage, fire or otherwise.
Interestingly, the author of the Prima strategy guide was apparently unaware that the attack can be aimed, even though the move has been aimable throughout the entire series; he suggests that its only use is attacking players from beneath.
Firedashing is a nearly useless Fox technique discovered by Hylian that involves using Fire Fox to bounce off of the stage and edgehog. The technique is present in both Super Smash Bros. Melee and Brawl.
To perform the technique, the player stands on the stage, facing the target ledge. They then jump and use Fire Fox diagonally into the stage, heading towards the ledge. Upon collision, Fox will bounce off the stage and, if spaced properly, fall right to the edge. If the player holds the control stick/d-pad back (towards the edge) as Fox falls past it, he will grab onto the edge, thus edgehogging.
However, given that the technique requires incredibly precise spacing, anyone who can aim Fire Fox that well could just as easily use it directly to the ledge, because Fox/Falco's up special moves will grab onto the edge from any direction as long as the control stick/d-pad is tilted towards the ledge when they encounter its sweetspot radius.
Special Move customization was added in Super Smash Bros. 4. These are the variations:
While Fire Fox (and clones thereof) is unique to Smash Bros, the way Fox is surrounded by flames while executing the move is similar to how a spaceship enters a planet's atmosphere. As Fox hails from Star Fox, a video game series about spaceships, this would make plenty of sense. Alternatively, the move's fiery nature may be related to the powers of the fox-like creature of Japanese myth, the kitsune; Fox's creator, Shigeru Miyamoto, confirmed that Fox's creation was partially inspired by the foxes of Fushimi Inari-taisha.
In Star Fox 64 3D, an aesthetically similar power-up called Firebird and exclusive to Battle Mode had been introduced, over ten years after Fire Fox being featured in Super Smash Bros. It is a very rare power-up that makes the Arwing surround itself by flames; it is extremely powerful, instantly destroying any opponent entering in contact with the user. However, it is unknown if the Firebird power-up had actually been inspired from Fox and Falco's up special move from the Super Smash Bros. series, or if it is just a coincidence.