Hitstun is the period of time after being hit that a character is unable to act outside of directional influence or teching. Hitstun received is a function of knockback and so is essentially also linked to the distance travelled before action is possible. At knockbacks low enough to not cause tumbling, hitstun is equal to the length of the flinch animation, while at higher knockbacks it is a straight multiplier of the knockback received.
Hitstun is an essential component of combos, with the point of a combo being that the target is trapped in the hitstun of consecutive attacks. As a result, games that have more hitstun for equivalent knockback open up more potential combos.
Brawl allows characters to attack and airdodge during hitstun (after a certain minimum amount). It is unknown why this was implemented as it completely defeats the purpose of the mechanic and allows momentum cancelling. It is one of the most controversial additions to Brawl, with detractors criticising it for making combos much rarer, skewing character survival rates, and even allowing characters to get punished when landing a hit.
The amount of hitstun, measured in frames, is equal to 0.4 times the amount of knockback. Button mashing has no effect on it.