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 two-thirds 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. Bowser can uniquely take advantage of crouch cancelling with Tough Guy, his unique form of passive knockback-based armor; he will not flinch for a wider range of percentages from weak attacks while crouching.
Crouch cancelling is equal to in SSB4, with a knockback reduction of 0.85x and a freeze frame reduction of 0.67x. However, the attacker's freeze frames are now also reduced by the same amount.
In addition, attacks in Ultimate (as well as SSB4) generally have much higher base knockback than in older games; this means that, even at very low percents, crouch cancelling usually cannot reduce launch distance enough to allow a punish afterwards. For these reasons, it has very little usefulness in competitive play. It can, however, allow players to avoid tumble until higher percentages, most notably with super heavyweight characters such as Bowser and King K. Rool. Additionally, Bowser retains Tough Guy from Super Smash Bros. 4, and newcomer Kazuya possesses an almost identical mechanic, dubbed Tough Body. As Kazuya has also access to a variety of attacks that can only be used while crouching, he can make use of crouch cancelling, with or without the effect of Tough Body, more often than most other characters.