As TM and I would put it,
ATB stands for “Active Time Battle” with VATB representing “Variable Active Time Battle.” The background from ATB stems back from this gaming parlor my brother and I would go to. ATB is actually a combination of many types of games with Axis and Allies, RPGs, and Magic at the forefront. It is based on the theory of time management. If I am able to perform more actions than my opponent within a given set of time, then my chances of victory increases dramatically. VATB, however, is a much newer design that incorporates ATB into the economy. What it is saying is that if the battlefield changes dramatically than I am able to make the changes appropriately to match the new environment instead managing my economy in a paper-conformist attitude.
When you look at Axis and Allies, you can break in down into different types of ATB. One revolves around Action. Under Action-ATB, my moves will generally control the tempo of the game. I can choose between scatting, which is going after many different territories at once or blocking, which is focusing on one particular territory. Since I am the one who is performing the actions, my opponent will be force to react to my actions with that of his own. This brings to the second type of ATB, Countering. Countering would be where I watch my opponent unfold his turn and then counter with my own. An example would be if Germany was building a submarine force, I, as UK, can counter that move by building a naval force of my own or building a air force. Obviously, each type of ATB has its own faults and merits.