The Atkinson cycle is a variation of the conventional (Otto) cycle which most engines use. It is used in some naturally aspirated engines, and is similar to the Miller cycle, used in some forced induction engines.
Atkinson cycle engines are designed with a high geometric compression ratio, but the intake valve timing is altered so that the valves are left open after the piston starts to rise on the compression stroke. This allows some intake charge to flow back into the induction system, effectively reducing the compression ratio and pumping losses. But the geometry of the engine means that the expansion ratio is high, leading to high thermal efficiency.
Because the full cylinder capacity is not being used by the Atkinson cycle, its maximum power is less than the Otto cycle.