Same reason a wider intake pipe or a fatter exhaust pipes increase horsepower, by reducing airflow resistance. That's not the issue here. I you run with no filter at all you will increase your horsepower slightly just due to lower drag on the intake stroke.
As I posted, it's not an air "resistance" issue, it's a resonance issue.
Engines are pulsing instruments and with various length and width pipes on the intake and exhaust and various RPMs, you will approach resonant nodes or harmonics that reduce restriction for a while, similar to playing a flute and getting the air you're breathing to properly match the resonance of the flute. When you hit it, BAM, you've got smooth air flow and music. Filters have little or no effect on resonance.
Exhaust test-pipes that "make power" generally do so for the same reason, because they improve the resonance of the exhaust line. That's why "high-flow" cats rarely make power. They only change blockage, not resonance issues.
You can find dyno videos on youtube of people building experiment intakes that are like six feet of solid tubing reaching into the sky. The longer tube gets the resonance down really low and lets the breathing approach more acoustically tuned nodes than a short tube, similar to a pipe organ. They make power that way, but of course you can't actually drive anywhere with one of those things.
Intake and exhaust breathing has more to do with acoustical science than it does with reducing "blockage".