Auto-canceling is the act of landing during the beginning or ending frames of an aerial attack, thereby circumventing the landing lag that would have occurred had the character instead landed during the middle of that attack's animation.
Auto-canceling an attack produces no more landing lag than a regular landing from an ordinary jump (of which the landing lag tends to be around 4-6 frames, a very short amount of time), whereas landing during the middle of an aerial attack almost always results in a significant delay before the character can act (raise a shield, jump, dodge, etc.) again. Most aerial attacks can be auto-cancelled during both the first few frames and the last few frames of the attack's animation; however, some attacks cannot be auto-cancelled at the start, at the end, or even at all. If an aerial does not have a late auto-cancel window or if the auto-cancel window occurs after the animation has ended, the aerial will auto-cancel once the animation has finished. Each individual aerial attack for every character has a specific auto-cancelling window (or lack thereof) that must be memorized and practiced.
Auto-canceling can be very beneficial to players using characters with laggy aerial attacks, as this can reduce the amount of landing lag produced, and create more time for the character to act, potentially avoiding being punished during the move's landing lag. Precise auto-canceling of aerials is also frequently needed for performing followups and combos, so as to leave less time for the opponent to react and escape.
In Super Smash Bros., auto-cancelling generally has no large impact on gameplay, since L-canceling practically has the same effect although some moves do have extremely lenient auto-cancel windows. A notable example is Ness's down/up aerial which will always auto-cancel. These moves can be used for shield breaks which requires many inputs so the lack of needing to z-cancel makes the shield break significantly easier. All aerials except for Link's up and down aerials are capable of auto-canceling in a short hop.
Super Smash Bros. Melee reduced the effect of L-canceling (now only having the landing lag as opposed to reducing it to 4 frames) making auto-canceling more useful although jumps are shorter than they were in Smash 64 due to gravity being increased across the board and auto-cancel windows are far less lenient across the board making a lot less aerials capable of auto-canceling in a short hop.
Super Smash Bros. Brawl removed L-canceling making auto-canceling more important and useful as while numerous aerials have lower landing lag, none of them had their landing lag reduced enough to completely compensate for the removal of L-canceling. Aerial attacks in Brawl generally have more lenient auto-cancel windows to partially compensate which is further compensated by gravity/falling speeds being much lower than in Melee. A lot more aerials can be auto-cancelled in a short hop in Brawl compared to Melee because of these changes.
In Super Smash Bros. 4, L-canceling continues to be absent, and aerials overall have slightly increased landing lag and later auto-cancel windows, hindering aerial approaches and enforcing a heavier reliance on grounded combat. While some aerials gained the ability the auto-cancel in a short hop, a majority lost their ability to do so either because of their worse auto-cancel windows, the character's lower short hop or both.
In Super Smash Bros. Ultimate, however, since the landing lag on moves has been altered and substantially reduced across the board, aerial approaches have become safer than previously. Aerials are also considerably weaker when performed during a short hop with these changes overall making auto-canceling less useful depending on the aerial. However, many aerials (e.g. Falco's down aerial) have improved auto-cancel windows enabling them to properly auto-cancel in a short hop although naturally, the opposite is also the case with some aerials (e.g. Ike's forward aerial) and some characters are now unable to auto-cancel certain aerials due to their higher gravity reducing the height of their short hop (e.g. Charizard's forward aerial).
The following characters' respective moves have notable auto-cancels.
List of characters who can auto-cancel all aerials in a short hop