The way I understand it goes something like this...
Higher quality cables help do 2 things:
- reduce internal and external interference, and
- transmit the signal without loss
In the analog world the topic of "are those expensive cables worth it?" is certainly debatable. Personally I do not have the ears to tell the difference so I get the mid-range stuff (not the cheapest that anyone could ever get away with, but not $20 a foot either).
BUT when it comes to digital it's a whole new ball game. Your HDMI source, lets say a BluRay player, is more or less pumping out "1s" and "0s", or more accurately "Ons" and "Offs". So long as the device on the other end of the cable can tell whether it's been delivered a "1" or a "0" is all that matters. I don't know how much influence interference can have on the signal, but with digital it would have to be enough to turn the 0s and 1s into "0.5s" (a bit where the receiver cannot tell if it's "on" or "off").
I'm reminded of this image from
SpinRite, an excellent data recovery tool.
The progression of different digital media (CDs, DVDs, HD stuff, etc.) is a different topic altogether. For HDMI cables the only question is: do the 1s and 0s make it to the other end or not? With digital, this is easily tested scientifically.