While in blockstun, press forward and A+B simultaneously to perform an action that cancels your guarding animation with a counter, akin to how most similar mechanics work in other fighting games. The types of recoil differ depending on the character, but while countering the opponent, the player is invincible. Note that if the Counter Assault is blocked, the player will be vulnerable for a long period. Counter Assaults also cannot inflict any killing/fatal damage regardless of the victim's health amount.
However, some Counter Assaults, like Noel's are considered unique in that they may not be an offensive attack; her's works akin to a guard-cancel-type-evasion move instead.
This move consumes 50% of Heat Gauge, though with later versions of BlazBlue: Continuum Shift instead also depleting half of the total user's Guard Primers as an extra cost.