There are some good responses, but this has been asked and answered so many times so a search might help avoid a new round of "heads in the sand".
Also, this is a fun name calling and pot-shotting topic for arm-chair paper tigers so its hard to sort through the BS when asking seemingly straightforward questions.
Here are a few simple, straightforward explanations in layman's terms..
One of the fundamental reasons any decently designed after-market power cord can make a difference is that noise generated and shared within interconnected systems poses a far greater challenge to resolution and fidelity than externally generated AC interference. Just as it is within electronics themselves, the laws of proximity rule when it comes to the effective treatment of radiated and power supply generated noise.
Power cords are designed to act as sympathetic, noise-isolated extensions of the primary winding within a components power supply. Seen this way, their function takes on a more understandable role. They represent the initial outward electrical interface for each piece of electronics in the system. That raw wire interface can either act as an antenna for radiated HF and ground-borne noise or it can be engineered to isolate the power-supply port from internal and external EMI, RFI interference.
There is no such thing as a power supply that is adequate to filtering or isolating itself entirely from the huge volume of gigahertz noise that surrounds electronics systems and comes from within them. The bigger and more powerful the system, typically the larger the problem an unshielded or unprotected AC port can become. That is not to say electronics systems cannot sound great without after-market cords, or that tons of money must be spent on them, it's just to say that there is real-world science that explains why that they "can and most often do make an easy to hear difference or improvement in recorded or reproduced sound".
In general, power cords do not represent the last few feet of an AC grid leading to a component; they are first few feet from the perspective of each components power supply. Due to the fact that your AC is in principle the_source_ of sound for any music or sound system--AC rectified to DC which carries the signal through the system--it would seem imprudent to ignore the possibility of a difference and not perform the simplest of empirical experiments for oneself--unless the point of discourse is only to make funny asides under strict internet protection :o).
Since no product of this or any kind are being forced on anyone, each is free to try for themselves and make their own determination. Certainly the fact that many of the finest recording studios, mastering professionals, electronics engineers speaker manufacturers openly use and endorse them would seem to dim some of the more ardent "internet posting professionals" erm, arguments...
Grant
Shunyata Research