Super Canceling, often abbreviated as "SC", is a mechanic introduced in the Street Fighter III series, but has also been implemented into other fighting games as a mainstay mechanic ever since.
Super Canceling makes it easier to string together higher-damage combos than simply performing the Super Art/Super Combo on its own. The damage done by the Super Art/Super Combo itself is lowered; this is due to the programming of Super Cancels in the Street Fighter III series, and damage scaling in the Street Fighter IV games.
The Street Fighter EX series expands upon the Super Cancel mechanic, allowing a Super Combo to be cancelled into a different Super Combo, as long as the player has enough meter.
In other kinds of fighting games, SC'ing during special attacks usually requires a form of extra cost for the super that's being cancelled into, as opposed to the usual criteria for when it's performed standalone or chained/cancelled into from a normal attack. Both other fighting games and the Street Fighter games alike make this a very character-dependent-based mechanic, as they are unique for each character and for each of their moves. Examples often include only certain projectiles being SC'able just as they come out or moves that are SC'able during certain frames upon connecting. There also exist moves that cannot be SC'able at all.
Super Cancels have evolved in crossover games such as Marvel vs. Capcom 2 and its two sequels, in the form of Delayed Hyper Combo, where team members can cancel a currently-performing Hyper Combo into another Hyper Combo from another member, up to 3 times. It is a staple game mechanic and is used either for extending combos, increasing damage output (especially in Marvel vs. Capcom 3 and its Ultimate upgrade, where Lv3 Hyper Combos deals unscaled damage), as a safety move, if a character does a Hyper Combo that misses and is left open for an attack, or even a trick/bait tactic, making the opponent drop their guard by mistake, only for the player to switch to another of his/her character's Hyper Combo that deals more damage and can hit anywhere (a notorious example of this is DHC from anyone's Lv1 Hyper Combo to an omni-hitting Lv3 Hyper Combo, such as Phoenix Wright's Ace Attorney Hyper Combo, or Magneto's Gravity Squeeze).