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.