professorhat:
Digital or not, it mostly comes down to "how" a signal is transmitted. For example, a lot is made by digital naysayers that digital information is sent over the internet with no loss and thus, signals sent over small distances cannot possibly be affected. However, in the case of the internet, a protocol called TCP/IP is used which was developed by the US military in the 60s / 70s in anticipation of World War III when it was expected that data loss over networks would be high due to nuclear incidents destroying much of the required infrastructure. As a result, this digital transport protocol is highly resilient and thus perfect for long distance communications over the internet. On the other hand, it would never be used over local networks (unless the product was designed to work on both local and slow networks), since the high speeds mean less resilient protocols could be used with error control without the end user being aware.
When it comes to digital hi-fi / home cinema signals, I have to admit to being completely in the dark on how they are transmitted. However, I do know that an HDMI signal is in the region of several Gbits per second which is a huge amount of data (in orders of magnitude above your average PC user), and also, given the nature of home cinema, there is no window for pausing when it comes to error control. To put it in perspective, if you're downloading a web page, the browser is using TCP/IP and thus there are no qualms in making you wait an extra few seconds before displaying that web page to error check everything received and ensure your web browser has received all the details exactly as they were transmitted from the original site. When it comes to playing a Blu-Ray movie though, the amount of data being transmitted is likely at least a thousandfold more than your average web page and then the player doesn't have the luxury of stopping the playback, error checking what it's receiving, and then carrying on the video - can you imagine the outcry if this was how Blu-Ray worked?!
As a result, the better HDMI cables (note the word better, not necessarily more expensive), deliver a signal with less errors which is closer to the original stream sent from the Blu-Ray player and thus, the error control software has less to guess and you get a picture which is closer to the one deigned by the director / producer of the movie.
Very well put Professorhat! I am no expert in this field, but your description and analysis sounds plausible.