what does it mean by

Well, it may sound stupid, but I don't know exactly what it means by. Does it mean by connecting a power cable of an audio component directly to the power receptacle without using extension cord?
Normally a power receptacle provides two connections. Would there be an interference if power cords of two audio components are connected to the receptacle?

What exactly does it mean by dedicated power line?
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A dedicated circuit is one that is not shared by any other electrical devices in your home and is used solely for your audio system.

Tv's usually cause noise in audio systems.
You definitely don't want to be in the same circuit (same fuse or circuit breaker) with any appliances.
Also, even if there is no other device drawing electrical current from the same electrical circuit at the same time, some manufacturers might recommend not using an extension cord because:
1) some extension cords are not rated for full wattage that a high-wattage Class A amp might draw at peak.
2) extension cords are generally not as safe (people trip over them) as the first 2 meters of power cord)
3) from what I have read in the past... if some other device is plugged in, even if it is not "on", it is possible that it may present a load to the electrical circuit.
The idea that a dedicated line is isolated from the rest of the devices in the home like TVs is incorrect. Everything is tied together at the breaker box so they are not isolated. If the TV or whatever injects noise on the AC lines then it goes all over the house. What a dedicated line will do for you is allow your stereo to draw power from the breaker box without sharing that line with anything else which theoretically allows it to breathe a little easier.
How about using serge protector? Would it make a dedicated circuit no longer dedicated?

I have 9 components in one setup -- power, pre amp, CDP, CD duplicator, dvd player, turntable, TV, receiver (for inwall speaker), and a laptop connected to the receiver for mp3 player.
There are two receptacles (total 4 connections) near the audio rack. I have a serge protector that has 6 outlets. If I upgrade the power receptacles, how may I arrange the power connection?
What I can think of is, to connect the power cords of the power and pre amps to one receptacle, and the turntable and power strip to another receptacle. Then, connect the rest of six power cords to the power stip outlet.
Any better suggestion?
Herman is pretty close to the reality of how most homes are set up. If you want a TRUE "dedicated line", it requires another input/breaker to your home from the outside. Now, the thing you have to remember is that this may not buy you much if the power in your area is cruddy to begin with. All you're doing is just installing another pipe of the same crud. It does allow the potential for more current draw, but you still wind up with the need to condtion the power.

Another technique that can help is to have an electrician install an "isolated ground" circuit for you. This is much more common and much more cost effective for most folks. What this does, is essentially put a circuit on it's own ground plane back at your input panel and isolates a lot of the noise and hash from the rest of your house because the ground line is separated. It still uses the same hot & neutral lines as everything else, but does help quite a bit.

Be very careful with surge protectors, especially cheap ones because they cause more harm then good most of the time. If you get a good conditioner (there's lots of them out there; PS Audio, Monster, Transparent, Shunyata, Balanced Power, etc,etc, etc, blah, blah, blah...!), one thing that is of utmost importance is that it does NOT limit current or at least does not limit current to any large extent. you may get cleaner power, but it will be choked off and you'll loose any benefit with a loss of dynamics and tonal accuracy.

My recommedation, based on the info you've provided, would be to plug your power amp directly to the wall. I'd put the rest of your audio components on a decent power conditioner and then put your TV on a conditioner or decent surge protector on its own so it's as isolated from the other stuff as possible. You could potentially put your power and pre together on a conditioned line to the wall as long as it doesn't limit current. Lots of times, you'll find that your power amp is best going straight to the wall so you have no limitation of current, but of course you run the risk of damage should you get hit by lightning or a power surge (that's what insurance is for!). The rest of the audio stuff is pretty much small signal and has lower power requirements, so they can go together without much trouble. I'd defintiely use something that isolates the TV as much as possible, although you're still limited by the fact that everything will be going into the same quad box at the wall. It is a little tricky, experiment, and remember that with electronics there's no free lunch! When you effect a change in one place it will cause an opposite effect elsewhere. Just don't get too wrapped around the axle and forget to enjoy your system! Good luck! :)
Many thanks to all. Now I have a better understanding of how to configure power connections. I will definitely try better power receptacles like Porter Ports and others later.