Regulated Power Supply- what does it do/mean?

I have pretty good quality components, amp, preamp, cd player. I also have a PS audio PowerPlant P-300, which regenerates the AC to make it a perfect 117 volt p-p sinewave no matter what the voltage fluctuation is from the wall.

On further thinking, my question is why do I need power regeneration if my preamp, amp and CD player have fully regulated power supplies (don't reply with other features of the P-300 such as multiwave or filtering)? Shouldn't a fully regulated power supply give you say exactly 20 volts DC even if the line voltage fluctuates? Isn't this the purpose of a "fully regulated" power supply or am I wrong? What is a "fully regulated" power supply?
A regulated power supply will send the correct voltage no matter what the input voltage may be. Inmany cases input voltage may vary with the time of day or year. It also may deal with noise spikes and other power issues.
There is a very nice 3 part piece on power supplies in the latest on line edition of "Valve" magazine which is part of the website

Your definition of fully regulated is correct. That brings up several considerations for a particular component

1. Does it use regulated supplies? Many don't. It is unusual to have regulated supplies in the output stages of power amps and many tube circuits do not.

2. Is the design really fully regulated? Is it capable of completely rejecting any and all variations in the incoming line?

3. Is it capable of completely rejecting noise that is not 60 Hz such as RF and spikes on the line?

If the answer to all of the above is yes, then a regenerater will probably be of limited benefit. For instance, Levinson reference components already have this function built in. On the other hand, a component with little or no regulation could concievably benefit from regeneration.
I believe that a "Regulated Power Supply", is approved by the FDIC, CIA, FBI, HUD and several other agencies. What they do is add several layers of additional government agency intervention in ways that have no impact on quality of life...but huge impact on the cost of living.