The King of Fighters XII’s Critical Counter mechanism has been shown and explained in Japanese at a Famitsu event:
Basically, if you perform a close-range counter attack (i.e. just after opponent is about to execute an attack on you), you will be able to stun your opponent monentarily and perform a string of combos which consist of cancellable moves.
As seen in the video, the resulting damage is significant with one such Critical Counter maneuver. That was what SNK meant when they mentioned prediction of opponents’ moves plays an important role in KOF XII.