After you read that wiki decription, this is what need to know.
Power Factor (pf) is a way of describing the amount of wasted energy potential in a system. Not necessarily wasted energy, but wasted potential energy. To explain that, you need to understand that the only people who truly give a rat's behind about pf are the people who supply and deliver power, i.e. the source, not the users.
If I am a user and I have a lot of induction loads such as AC motors, the way the motors use power means that my supplier must make more energy available than I am going to really use, energy that just needs to be there to excite my motor's windings. I am not using it to do useful work so the supplier can't bill me for it, but he has to provide it nonetheless. So for him, it is power he had to generate, transmit and deliver, for which he gets no direct revenue. It's essentially the cost of doing business for the utility. An often used analogy is to think of it like the foam on a glass of beer. When you buy it from the bartender you don't really want the foam and expect a full glass of beer. But in delivering the beer, the foam is created so the bartender has to poor it off, getting no money for it.
So back to the power provider, my poor pf means he has to generate ALL of the power, which we call apparent power, or kVA, but I only USE (and he can only meter) the part that does real work, i.e. the real power or kW. The provider then essentially gets stiffed for some of the generating capacity kVA he has made available to me.
So what most utilities do is to measure your overall average pf every month and slap you with a penalty for having poor pf by jacking up your power rate that month, essentially mitigating their costs of doing business with you without having to raise the rates for your neighbors who have better pf. It's sort of like a progressive tax; if you take steps to correct your pf, you avoid having to pay the extra tax.
If you owned your own generator, then poor pf will directly cost YOU money in increased fuel costs. In addition if you own your own transformers, it means you cannot utilize your transformer's capacity to the fullest because some of it is going to need to be there to make the downstream stuff work. So you have to have more transformer capacity than you are really going to use, which translates to lower efficiency, which costs you money. Or if you grow, you have to buy a bigger transformer and that costs you money too.
Correcting pf means having something, such as a capacitor, that captures some of that energy that is returned by the load (from the wiki description) and storing it briefly so it can be used in doing the excitation job that would normally need to be done by the utility power. So although it will not reduce the real work (kW) used by the load, it allows the utility (or your generator or transformer) to utilize the available power to it's fullest.