The double jump cancel, sometimes abbreviated as DJC, is a glitch-tactic used by Ness, Mewtwo, Peach, and Yoshi, who can attack immediately after their double jump to cancel their upward momentum and land on the ground soon after their attack. This tactic is used to perform aerial attacks incredibly quickly, thus allowing aerial combos and KO's to be performed more quickly. Double jump canceling has almost been completely removed in Super Smash Bros. Brawl, some specials are the only moves that can cancel character's midair jumps.
Ness
Ness' play in SSB64 is almost completely reliant on this technique. Because his aerials provide high hit stun and damage, he can perform zero-death combos on several characters. At one point this ability was even considered broken. However, it has since lost such recognition due to Ness' short range, but nonetheless is an important part of his metagame. In Melee, Ness still has the technique, but it is not as useful due to the nerfs he suffered in the game. In Brawl, Ness can no longer perform double jump cancel unless he initiates a special move. However, he can still pull of some techniques with this, such as PK Jump.
Peach
For Peach, this tactic is usable, but generally unused due to her slower aerials and superior float cancels. The pro Peach user XIF is known for using multiple djc's neutral aerial.
Yoshi
Yoshi's double jump cancel is extremely useful in SSB64, being able to pull of suprisingly fast dairs, and with the attack doing up to 30 damage, he can even get a 0-death combo with some characters.
For Yoshi, he can use this to "Counter" attacks because of his double jump's unique properties.
One obvious downfall of this tactic is that Yoshi loses his double jump, possibly resulting in a self-destruct when away from an edge. This can be extremely detrimental to him, as he lacks a third jump, and if Yoshi is hit away from the stage, Yoshi will have almost no means of recovery.
DJC physics
Since the affected characters' double jumps are of the "delayed" type (where they do not rise immediately), interrupting the action with an attack will cause the scheduled upwards force to not take place.
A similar mechanic can cause superjumps.
Double Jump Cancel Fast Fall L-cancel
Double jump cancel fast fall l-cancel (abbreviated as "DJCFFL") is a tactic that is simply a quicker application of the double jump cancel, and is most often used by Ness, Mewtwo, and Yoshi. It allows the character in question to attack aerially even faster than with a shffl'd aerial. This technique also plays a huge role in the Dragonic Reverse.
Execution
To perform this technique, the player must do their first jump, then double jump just as they leave the ground, and press A. The player's double jump will be canceled and they will do the attack and immediately fall. The player may fast fall almost immediately, and L-cancel the aerial very quickly. The result will cause the character using this technique to attack extremely quickly.