Here is why cables matter. Power to a lamp is just enough current to make a filament glow. It doesn't matter what the waveform looks like, whether there is noise on the circuit, or if there are losses/disruptions along the way. If the power gets to the light bulb, the electrician declares victory.
In a stereo application, we have 2 goals: signal and power. The signal path is sacred. You don't have just power running through there, you have all the detail of the music encoded into the electrical signal. each transition between materials, across junctions, bad solder joints, or even large mass changes such as speaker binding posts challenge the signal to maintain all that precious data. The better the wire, the more consistent the path, the less material or physical interfaces that the signal sees, the less it is disrupted. In a perfect world it would be a straight wire of silver running through a vacuum. So do everything you can to make the signal wire as successful as possible.
Power is less important but important just as well. There are 2 aspects of power:
1. adequate size of the conductor. The cable needs to be larger than you would think, even for a low power amp. this supports dynamic changes where current flow can be very high for a very short period of time.
2. Quality of connectors and 60 hz waveform etc. The quality of the power needed is often less important because manufacturers of great amps take care of this themselves but it can never hurt and using high quality cables can add. I think the 1st point above is 95% of it but others disagree and you can form your own opinion.
Jerry