Ok so air travels from an area of high pressure to an area of low pressure. Basic science. The low pressure is in the engine caused by the downstroke of the cylinder (im not very technical i hope this is right). This creates a pressure difference that alllows air to passively move from the air inlet manifold to the engine (this is in the standard case). A normal filter (paper) impedes this air flow particularly as it gets old, and this is the principle of a performance filter. The performance filter is less restrictive and facilitates an easier flow of passive air down its concentration gradient from the airbox to the engine.
Now, from a non techinical viewpoint with my scientific hat on, i would have thought that if you can increase the pressure in the airbox, you will in effect create a greater pressure differential between the airbox and the engine. The greater the difference between the area of low pressure and the area of high pressure, the faster the air will travel (this is basic meteorology). This increased pressure differential may allow a greater flow of passive air down the pressure differential from thew airbox to the engine. So im not saying that you ramming air into the engine. Im saying you are trying to facilitate the normal process by increasing the pressure differential from the airbox to the engine.
However, this does in fact assume that there is less air reaching the engine than it actually needs. i.e. there is no point supplying 150% of the air required by the engine, as it will only ever need 100%. So if a standard Willy gets 95% of the air it needs (perhaps due to a poor inlet pipe that is restrictive), you could by increasing the pressure in the airbox suupply the extra 5% and get a performance increase.
This is only theory. Please feel free to shoot me down in flames. Also i know where only talking 1 maybe 2 BHP, but i feel that if you can find 1 or 2 BHP in a number of areas, it soon adds up.