A 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, some aspect of the attack will be weakened.
Crouch cancelling reduces the amount of knockback and freeze frames dealt to the user (2/3 initial knockback and freeze frames in Smash 64 and Melee), often stopping their movement completely at lower damage percentages. Because the control stick must be held downwards in order to crouch, crouch cancelling also effectively guarantees a lower launch angle, due to directional influence reading the downwards motion.
Many characters use crouch cancelling to perform a crouch cancel counter (CCC), where the player performs a strong counterattack after crouch cancelling an incoming attack. In Melee, 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.
Instead of lowering knockback, crouch cancelling instead 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 (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 Smash 64 and Melee than in Brawl, however.
Crouch cancelling functions like how it does in both Melee and Brawl. The amount of knockback suffered by the user is reduced to 85% of its initial value and the amount of freeze frames suffered by the user is reduced by 33%.