Here's the longer answer; (this is going to get complicated, you might need a piece of paper and a calculator)
There are two kinds of power: "usable power," which is measured in killowats (kW) and "reactive power," which is measured in kilovar (kVar). The ratio of these two measurements (usable power consumption to reactive power consumption) is called "power factor." This measures how efficiently the devices in your home convert electric current (generated by your utility company) into useful output such as heat, or light, or mechanical movement, or whatever the electrical device is doing. The power factor gets smaller as reactive power increases compared to usable power. Electrical engineers often use the "beer foam" analogy to explain power factor (which I noticed referenced on the site you linked to, although they misused it and totally failed to explain it, it's just a pretty picture they hope will help relieve you of your money, "hey...I like beer, they said something about beer...must be true, right?")
Usable power is like the liquid that fills most of a glass of beer. Reactive power is like the foam at the top of the glass. What you really want is the liquid, but the foam is there. You can’t avoid it but it doesn’t change the amount of beer at the bottom. Suppose you start with a glass with 12 ounces of beer, if there's a little foam at the top, the glass has to be slightly larger than the 12 ounce volume of the beer alone to contain it all. Suppose you shake the bottle and generate extra foam before you pour it into the glass, (also suppose it doesn't explode in your face when you open it) you haven’t changed the amount of beer, but you need a bigger glass to contain it all.
These snake oil companies usually claim that your power factor is "out of synch" and show you graphs of sine waves or talk about electron orbits or some such nonsense. There's no such thing, there's nothing to be "synched," it is what it is. Usable power and reactive power add up (well, trigonometrically) to give "apparent power." Where reactive power comes into play is in devices that generate magnetic fields; electric motors, transformers, fluorescent light ballasts, and things like that.
Ok, it's math time. Take a sheet of paper, and draw a horizontal line about one inch long. Label the left endpoint of the line as (1) and the right endpoint as (2). From (2), draw a vertical line upwards one inch. Label the endpoint of that line as (3). Finally, connect (1) and (3) to form a right triangle. Line 1-2 represents the usable power, and it measures the real work being done by the loaded equipment. Line 2-3 represents reactive power, and it measures the energy exchanged between the magnetic field of the utility company's generator and the magnetic field of the customer’s motors and various inductive loads. Line 1-3 represents apparent power, and is a measure of the power that the utility company has to provide in order for the customer to run their devices. Power factor (PF) is a measure of the angle located at point 1. In trigonometric terms, PF is defined as the cosine of that angle. If that angle is zero degrees (which it will be if line 1-3 has no length at all, so that line 1-2 and line 1-3 lie directly one on top of the other), then PF is "unity." If that angle is large (which it will be if line 1-3 is long), the PF is considered “poor.â€
Now what happens to that triangle, if you draw the vertical line (2-3) as 2 inches long, instead of 1 inch? The real power (line 1-2) does not change, but the apparent power provided by the utility company (line 1-3) is now much longer. In order to allow the customer’s motors to do the same amount of work, the utility has to provide more power. What happens to the triangle, if you draw the vertical line as 1/2 inch long, instead of 1 inch? Again, the real work (1-2) does not change. But the apparent power provided by the utility (line 1-3) is now much shorter. In order to allow the customer’s motors to do the same amount of work, the utility has to provide less power. You can see why the utility does not like the customer to have a lot of reactive power in their loads. You can also see why the utility charges some customers (large industrial plants, for example) a steep penalty for having a poor power factor. Industrial customers that have huge productions lines with a LOT of motors or many welders are charged for poor power factor. Bowling alleys are notorious for it, they're FULL of high torque electric motors. But there is nowhere in the world that utility companies charge residential customers for poor power factor.
What a "power factor correction device" (PFCD) does is reduce the length of line 2-3. It does that by adding a reactive load of a type that is opposite the customer’s loads. A customer’s loads are usually inductive loads. To that you add a capacitive load. That's all that's in your $500 box, a $1 capacitor. This is going to affect our triangle. Starting at point (3), draw a line downwards towards (but not as far as) line 1-2. Call the endpoint of this new line (4). Now Line 2-3 is the customer’s inductive loads. Line 3-4 is the power factor correction capacitors. Connect (2) and (4). Line 2-4 is the new value of total reactive power. If you connect (1) and (4) you get the new value of total apparent power. Notice that line 1-4 is shorter than line 1-3. So the amount of power supplied by the utility has gone down.
What is physically happening in the power factor correction device is that, where you used to have an exchange of energy between the between the magnetic field of the utility generator and the magnetic field of the customer’s motors and other inductive loads, you now have an exchange of energy between the magnetic field of the customer’s motors and the electric field of the power factor correction capacitors. Unfortunately for your bill, the utility company's meter does not record that energy exchange because it takes place ENTIRELY within the customer’s house. Since you are charged in kilowatt-hours (kWh) and NOT amps, and since you're not an industrial customer that is penalized for poor power factor, your bill at the end of the month will be exactly the same as it would have been before you plugged your magic box into your house (actually, your bill will be MORE because you paid $500 for a magic box that does nothing).
That's an exhaustive explanation, I realize, and we got pretty heavily into some theoretical concepts that are hard for a lot of people to grasp, but you MUST arm yourself with knowledge in order to combat the greed heads and pushers that want nothing more than to separate you from your money. The only way to reduce your electric bill at the end of the month is to reduce the amount of power (in kWh) that your house consumes. There IS a simple device that you can install all over your property that will do this, they've been around for years, they're called "off switches," and they work wonders.
