After reading the C&D article snippet I think I can offer a decent explanation.

Essentially you would need an engine that is able to operate in two combustion modes: HCCI and "regular." During low-load driving the engine runs in HCCI mode which has very low fuel consumption. When extra power is needed the engine kicks over to regular combustion mode. Overall, the engine uses less gas because it is only running in regular combustion mode when the driver requests extra power, and the rest of the time it's in HCCI.

Think of it like the SpeedStep technology that was used in some of Intel's mobile processors. When on battery power, the processor would have a low baseline clock speed for basic operations, and then when the user started to do something that required more computing power the processor would ramp up to a higher clock speed to get that work done more quickly. So instead of always running at that higher clock speed (i.e. normal combustion on the HCCI engine) all the time, it is able to run at that lower clock speed (HCCI combustion) when the extra grunt isn't needed.

Make sense?