A 2 circuit Dominator just has an idle/transition circuit and a main circuit.  
A 3 circuit Dominator has an extra intermediate circuit.  That circuit is based off of little tubes above the throttle blades.  When the throttle blades open, it adds fuel.  
In a lot of cases the 3 circuit Dominators are hard to get right on street cars and in most race applications.  Most of the carb builders I know prefer the 2 circuit carbs, although a good carb guy can make a 3 circuit carb run ok.  
Some of your really high end carbs can be 4 circuit or 5 circuit.