Pivoting, or DA Dashing, is a technique in Super Smash Bros., Super Smash Bros. Melee, and Super Smash Bros. 4 that lets a character use attacks out of a dash. The tactic was discovered originally in Melee by Philly Billy.
The technique makes use of the time frame at which a character turns during a dash; any normal ground options are available as if the character were standing still - smash attacks, grabs and tilts can occur here without the lag that usually comes from using these attacks after a dash. Normal pivoting is primarily used so that a character can quickly change the direction they are facing whilst not suffering the usual turn-around lag that would occur when doing so. This can allow characters to improve the utility of various moves in certain situations.
One use of pivoting is to dash a short distance away from an approaching opponent and then turn around to attack them with a forward tilt, forward smash, grab, or aerial. This is particularly useful for characters with disjointed attacks or far-reaching grabs. Pivoting can also be used to quickly put the player in a position to punish rolls and techs, as pictured. One specific use of this technique is for Marth's forward throw into forward smash. Typically the Marth would forward throw, wavedash, and then forward smash. With pivoting instead of wavedashing, the player can bypass Marth's jumpsquat frames and landing frames allowing Marth to use forward smash much more quickly than if he were to use wavedashing.
In Smash 64, pivoting off platforms makes it possible for characters to grab the ledge and proceed to edgeguard. This is known as a pivot ledgegrab. This is especially useful for Captain Falcon and Fox due to their long dash animations and fast falling speeds, though other characters are also able to use this technique. Captain Falcon, and to an extent other characters, can also make use of pivots in combos by comboing a forward throw into a pivot up aerial resulting in low percentage kills due to how powerful the semi-spike hitbox is. Outside of helping with combos, multiple characters have very useful pivots otherwise as part of their neutral game. A prime example of this is with Kirby where pivoting is used to fully exploit his up tilt hitbox.
A similar technique in Smash 64, the teleport, requires similar movement as pivoting.
It is also possible to perform a pivot without attacking, causing the character to simply stop and turn around without any lag. This is known among SSB4 players as a perfect pivot. A perfect pivot is borderline frame-perfect, so it is extremely difficult to do, especially with the flat analog stick on the 3DS. However, if a player can perform perfect pivots with consistency, the perfect pivot has potential use as a spacing move in competitive play. By performing a perfect pivot, a character will end up having moved backwards while still facing the same direction, and being able to attack right out of the perfect pivot. The distance the character covers depends on the character being used.
Pivoting with most attacks in Smash 4 is generally less forgiving than in 64 or Melee, as initial dashes are universally shorter between all characters, and most characters do not have good enough interruptibility on their initial dash to turn around afterwards for a pseudo-pivot. However, in Smash 4, pivot grabs can be done at any point in the run, and results in a grab with longer reach and more endlag than usual. Such pivot grabs can also be performed in Super Smash Bros. Brawl, where pivoting is otherwise not possible. Oddly enough, pivot forward tilts and forward smashes are only possible after a certain point of the initial dash (when the turn-around animation begins to occur), and they will also slide a large distance during their execution.