So looking at how "power factor" is calculated based on CampFussel's link, I think I can shed a little light on what this is and what it means in terms of engineering/physics.
Kinetic energy is equal to .5*mass*velocity^2 (image below for clarity). Units for this are typically foot-pounds or joules, which is what we normally use. Kinetic energy is the measure of something's ability to do work, that is to say it is the measure of a pellet's ability to do tissue damage (for example).
But there is something else: momentum. Newton's law, for every action there is an equal and opposite reaction, deals not in kinetic energy but in momentum. Momentum is equal to simply mass times velocity. You'll typically see it written as p=mv. Given the equations CampF shared, power factor is essentially a bastardization of momentum which makes numbers easier to share in shorthand as best I can tell.
Why does this matter to anyone? Well lets say you're a pistol shooter, and lets say you're trying to build loads to shoot defensively. You want the maximum kinetic energy, because that is killing power. However, you want the MINIMUM momentum, because that momentum is just recoil you have to deal with. Momentum is also what is transferred to the target in terms of this farcical "knockdown power." (people are no more knocked down by bullets hitting them than are the people firing the gun because momentum is conserved remember) So how do you maximize kinetic energy while minimizing momentum? Easy. Kinetic energy increases with the square of velocity, but momentum only increases linearly. Thus shooting lighter bullets at higher velocity will allow higher kinetic energies and lower momentum. It is important to note, in semi auto handguns with recoil operated actions (virtually all of them; handguns these days almost all use browning tilting actions to lock), your time in battery is based on the momentum of your projectile versus the momentum of your slide and barrel. As a result, you can tend to get away with higher pressures if you shoot lighter rounds because the lack of momentum working on the action keeps the weapon in battery for longer. I should also add that, competitive pistol shooting classes, sort people by "power factor." This is because it is easier to shoot a lower momentum handgun than a higher one, and so it is a way of balancing the playing field to keep people competing apples to apples.
Regarding power factor in airguns, I'm not sure it has any real usefulness. None of us are struggling to handle recoil, or talking about "knockdown power," so while a weird flavor of momentum is a tool in your toolkit to look at just what is going on with your rifle/projectile, methinks if you don't already know what it is, it probably isn't that useful to you. Just a guess though, I could be completely wrong and there may be some secret sauce hidden significance of power factor I'm not aware of.
I hope that helps.