Crouch cancel
A crouch cancel (or CC) is a technique in the 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.
In Super Smash Bros. and Super Smash Bros. Melee
Crouch cancelling reduces the amount of damage and knockback dealt to the user (2/3 initial knockback in Smash 64), often stopping their movement completely at lower damage percentages. Crouch cancelling has the added effect of lowering the trajectory of the player's character is sent after an attack (partly because of DI'ing downwards).
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 the attack that are not normally dealt. This is famously demonstrated with Peach's down smash, which deals a staggering 88% damage maximum on characters that crouch cancel.
In Super Smash Bros. Brawl
Crouch cancelling acts considerably more different than it does in the two previous games. 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.