Online desynchronization (sometimes shortened as desync or desynch) occurs when the perspectives of multiple players competing in one match are inconsistent with each other. The concept is best explained by example:
Once a match is desynched, the players are essentially playing different matches. Inputs will be sent and acted upon as usual, but the results of the inputs can be wildly different - a control stick input might be a down throw on one system and a fastfall on another. Re-syncing a match is sometimes possible, but requires extensive co-ordination between the players involved, and the cause of the original desynch will likely cause another disconnection later.
Brawl can disconnect players when it detects a desynch. When playing online, the games send information about the actions performed, mostly, but they can also send information that a loadable element has finished loading. If a match is desynched, a player may open a Smash Ball on one screen, but not on another. On the console where the Ball is opened, the game will load data for the corresponding Final Smash, and will send all other players a message saying that the Final Smash has been loaded. Since on the other consoles no Smash Ball has been opened, and no Final Smash had to be loaded, this "loading successful" message is treated as a mistake. After around 10 seconds, it's acknowledged that a desynch has inevitably fallen into place, and all players are disconnected.
Desynches are generally caused by hacks. Players using identical hacks generally does not cause desynch, but any hack that not all players share carries a risk of desynching. Some categories of hacks, such as textures, carry very little risk of desynching, while things such as model hacks are very likely, and moveset and physics hacks are guaranteed to desynch. Desynching also prevents players playing a proper match online using Brawl mods, such as Balanced Brawl and Brawl-, unless all players use the same mod. The effects of this type of desynching can also be viewed by watching the same saved replays while using different hacks/mods. In Super Smash Bros. for Wii U, the player using a hack is instantly disconnected from the match upon using a move that could desynchronize the game.
Desynchs can also happen if one of the participating players or the server is experiencing connection difficulties. This is normally rare, as most networking devices have built-in safety measures, created for the purpose of avoiding the sending and receiving of incorrect data, but given the amount of data that's sent per match, and given the variety of players and their hardware, as well as the fact that perfect connection conditions can't be met all the time, this type of the desynch is not completely implausible. This happens when, for instance, Alice presses X and A at the same time, but for some reason, one of the bits isn't sent (and, as described above, the hardware fails to catch this flaw), her console could end up sending data for only A being pressed. While in her console, she sees her character jumping and performing a neutral aerial attack, other players' Wiis will only receive the A button, and hence, will have that player's character perform a neutral attack.
A common error noted in replays is that they may "desync" over time; the effects vary, though among the most common are actions occurring that did not previously occur, excessive lag followed by significantly increased playback speed, and the replay abruptly ending. With the Pokémon Trainer, particularly unusual effects can occur, such as him sending out a Pokémon which never loads or leaves the revival platform. Replays of Wi-Fi matches are more likely to desync than local matches due to the frequent lag experienced in games, but local replays can also be subject to the problem. The cause of "desyncs" is unknown, though it is speculated it has to do with save data of replays becoming corrupted by some outside factor. In addition, it is possible for a replay that plays fine to randomly desynchronize when played again, and after some tries, play correctly again.
In Super Smash Bros. for Nintendo 3DS group matches, a rare glitch may occur that causes each game to load different stages for the same match, during which a 3DS may disconnect while the other 3DSs load the result screen. It is currently unknown if the different stage layouts can cause desynchs during actual gameplay.