Engine breathing is analogous to the breathing of any living organism. At rest, the lungs take in the necessary amount of air for normal function. When running, the lungs and heart work faster to supply more oxygen to the system. Engines can't do that because their breathing apparatus (comprised intake manifolds, intake runners, valves, valve lift and throttle bores) is fixed.
There was a time when engines had to be big to be powerful. There was a time when engines could either be tuned for low-rpm torque or high-rpm power, but not both. There was a time was a time when a specific output of 100 hp per liter was the stuff of race car fantasies. Today these limitations are all but gone. Getting 100 hp for each liter of displacement is now possible on cars that have to get good gas mileage, emit clean air, act civilized enough for your grandmother to drive them and sell for under $20,000.
Remember that an engine is basically a glorified air pump and, as such, the most effective way to increase horsepower and/or efficiency is to increase an engine's ability to process air. There are a number of ways to do this that range from altering the exhaust system to upgrading the fuel system to installing a less-restrictive air filter. Since an engine's valves play a major role in how air gets in and out of the combustion chamber, it makes sense to focus on them when looking to increase horsepower and efficiency. This is exactly what Honda, Toyota and BMW and quite a number of other manufacturer's have done in recent years.
Popet values are used in gasoline and diesel engines to control the inlet and exhaust of air passing through the engine. When the intake values open, air is drawn into the engine cylinder. After the fuel has been burnt, the exhaust valves then open to let it leave. In conventional engines, the popet valves open and close at a constant speed. Their timings do not depend on how fast the engine is running. At high engine speeds [e.g. when overtaking a slower vehicle], this starts to become a problem. Large amounts of air are required by the engine at higher speeds. However, the intake valves may close before all the air has been given a chance to flow in. On the other hand, if the valves were calibrated to remain open for longer periods of time, problems start to occur at the lower engine speeds. In these situations, unburnt fuel may exit from the engine since the valves are still open. This leads to lower engine performance and increased emissions. By using advanced systems to alter the opening and closing of engine valves, they have created more powerful and clean burning engines that require less fuel and are relatively small in displacement.