A critical hit is a term for an attack that staggers the opponent (this is referred to as a critical stun), instead of knocking them to the ground or launching them into the air. This allows for a series of follow-up of attacks, although all strikes will do 50% less damage. Staggered foes can still use holds (unless hit by what is referred to as a "forced sit-down"), but damage from holds during the critical state are reduced. Any strikes to a foe undergoing critical stun state is referred to as a critical combo. This is commonly used when performing combos, especially when used with critical bursts.
In Dead or Alive 5 and it's updates, when an opponent enters critical stun, a portion of their health bar flashes white to indicate the amount of damage that can be done to them before the critical stun is broken (i.e. doing more damage will either knock the opponent down or launch them). This amount is usually determined by how damaging the initial critical hit was; generally, a more damaging critical hit turns a larger portion of the opponent's health bar white and thus allows for a more damaging overall combo. Note that some strikes will floor or launch an opponent (thus ending the critical stun) even before the full damage limit of the critical stun has been reached. This may be used to juggle the opponent sooner and thus prevent them from holding. Also note that using the same strike twice in a row during a critical combo will always end the critical stun regardless of how much damage has been done.