Frames - The game runs at 60 frames per second(here after FPS) This means every second of real time 60 frames of animation occur.
There are 3 aspects to every move in the game regarding frames, startup, active and recovery frames. The startup frames are the number of frames it takes for a move to become active.(essentially how long it takes for the move to come out) The active frames are the amount of time the move is out.(essentially how long the move is capable of hitting your opponent or doing whatever else the move is intended to do). Recovery frames are exactly what they sound like. The amount of time after the move is no longer active until you are free to move,attack,block,whatever. Essentially how much time before you have control of your character again.
Your hitbox is your active collision. This is how the game registers hit detection. In MK9 all parts of all characters are always hot, meaning they can always be hit. However, not all characters have the same size hitbox, certain characters such as mileena and Sonya have small hit boxes and when crouching certain moves may whiff on them that wouldn't on larger characters such as Subzero or Freddy. Hitbox can also refer to the range on a given attack. Subzeros 2,2 string for instance has insane range on it. Its hitbox essentially covers Subzeros front, top and even a little behind his head.
Anti air is exactly what it sounds like. Any move that is reliable at knocking your opponent out of the air.