HCCI stands for Homogeneous Charge Compression Ignition. Basically, the fuel (gasoline) and air is drawn into the cylinder like in a normal ICE, but instead of using a spark plug to ignite it, it is ignited using a high compression ratio. The idea is to reduce temperature variations in the cylinder during ignition by having the whole cylinder go off at once rather than a flame front proceeding from the spark plug down, reducing entropy loss.

I'm surprised that Honda has an HCCI engine capable of commercial use. A lot of labs (including the one I'm working with) are still dealing with ignition control across a whole range of RPM's, and variable valve timing is just plain not flexible enough to control ignition times across all RPM ranges.