Volumetric efficiency is what we are going for with improved air filters.
The engine is sucking for air. Lessen the restriction on that suck, and more air /fuel volume gets sucked in. (i.e., the engine becomes more efficient)
That's all there is to it. If the guy is offering something with less restriction on the suck, the volumetric efficiency goes up.
Naturally, you also want filtration to be good too. These properties tend to be mutually exclusive, so at least equal filtration should be the primary concern, since most anything is usually better, performance wise, than the stock intake on most cars.