what does it mean by

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.

Wendell

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.