An air hitbox exists when a character is not on the ground.
Basically, during a jump, some special moves, some super special moves, and (particularly in KOF), during a backstep, one has this kind of hitbox.
In this state, one’s movements are restricted, but the damage one takes is subject to damage correction. Also, one does not take throw hitboxes other than from air throws and anti-air throws.
A typical technique taking advantage of this is the reversal backstep used by players in KOF.