Crouch cancel (or CC) is a technique in the Super Smash Bros. series used to reduce the effect of an attack on the user. By crouching before getting hit by an attack, the freeze frames will be reduced, as well as knockback in all games except Brawl.
Crouch canceling reduces the amount of knockback and freeze frames dealt with the user to 2/3rds its normal value, often reducing the effects to brief flinching at lower damage percentages. Because the control stick must be held downwards in order to crouch, crouch canceling also effectively guarantees a lower launch angle, due to directional influence reading the downwards motion.
Many characters use crouch canceling to perform a crouch cancel counter (CCC), where the player performs a strong counterattack after crouch canceling an incoming attack. Peach and Samus are well-known abusers of crouch cancel counters; both characters can crouch cancel most attacks and perform a down smash before their opponent recovers. Note that the reduced knockback comes with disadvantages, as it leaves the user open to hits of certain attacks that would not usually connect. For example, Peach's down smash may deal a staggering 70% damage maximum if all hits connect. While the attack was supposed to be designed such that only a single hit will make contact, it has a greater chance of happening against characters who crouch cancel, as they will not take enough knockback to escape the many hits of the down smash.
Here is a good tutorial for this techique: https://www.youtube.com/watch?v=72aidPrzScA
Crouch cancelling does not affect knockback, and instead only reduces the amount of freeze frames suffered by the user by 33%; the attacker's freeze frames are unaffected. This gives the target a small window of time in which to counterattack; for example an Olimar can crouch cancel the first hit of Falco's neutral attack in order to powershield the second hit and gain a free up smash.
Crouch cancelling is mentioned (though not by name) in the Brawl manual, stating that crouching "...stabilizes you, reducing the chances an attack will knock you back." This is more in line with the technique's behaviour in other installments than in Brawl, however.
Crouch cancelling functions similarly to Melee, albeit toned down. Under normal circumstances, the amount of knockback suffered by the user is reduced to 0.85× its initial value, and the amount of freeze frames suffered by the user is reduced to 0.67× its initial value. However, size changing items seem to reduce the knockback taken multiplier even further.
Although the technique's usefulness at low percents is limited, it is still fairly useful for survival at higher percents, especially with the more polarized knockback of smash attacks and other KO moves.
Crouch cancelling has been amplified back to its effectiveness in Melee, with both knockback and freeze frames suffered reduced to 0.67x their original values. However, the attacker's freeze frames are reduced by the same amount, eliminating the technique's use for counterattacking.