The power wiring in the wall will usually have harmonics of the 60 hz from radio signals, motor back-feed, fluorescent ballasts (which add current to the neutral), and other electric fields from power users on the same grid (elevator motors and machinery in the building across town.) All this noise gets into your power supply. The ability of the PS to reject this noise varies in proportion to its cost. Also, digital switching generates noise from within the cdp, further adding to the problem. The active circuitry gains up any signal, including noise, which is passed along as distortion to the components downstream.
A good power cord will filter some of the ac noise entering the power supply. This can reduce the noise from from coupling to the active circuits via stray capacitance and being gained. It can also reduce the noise generated by the cdp from reinfecting the power wiring by filtering the EMI/RF fields both from the cdp and common mode noise that can couple onto the power cord.
I have noticed the greatest improvements in digital front end from power cords that do a good job in filtering noise, such as the MIT Z-II cords, for the above reasons - I think. Cords which do the same job of filtering for a lot more money should be looked at with hand guarding wallet, IMO.