I thought I'd read that the amplification was only turned up when you enable those extended ISO modes that most DSLRs have.
Yes, I thought I read the opposite some time ago, but I was not particularly interested in the topic at the time and may be remembering wrong. In any case, I thought that the bit-shift Dan mentioned was in fact the "extended" ISO modes, while the ISO setting per se consisted in - that is the way I remembered - changing some "hardware" operating parameter on the sensor itself. Mark's amp voltage change explanation seems to fit well what I remember. Of course, I really don't know. I am mostly learning how this works as we speak.
In either case, I wonder why is Nikon D800 ISO sensitivity is reported 100-6400, while Canon 5DIII is 100-25600 (again, I am just curious to understand how it works, no intention to prove any specific product "better").
If ISO setting is as Mark indicates, one may argue that Sensor+amp circuitry on some cameras be good enough to allow workable pictures at higher ISO, while some other sensors+amp are not.
If ISO setting is only software/firmware based, as Dan suggests, then I can't find a reason why Nikon shouldn't push the settings all the way to 25600, a good marketing tool regardless, right?