I'm not sure I want to get into the previous argument, but I can take a stab at this one.
HDR as it's being used in regards to the PS4 Pro and UHD Blu-ray really refers to two different things.
One is brightness range, this is what's normally meant by HDR. Ignoring color, it allows a picture to have bright areas and dim areas while still having discernable detail in both. Standard displays only have 256 brightness levels, so there's not a lot of room to play with brightness. It's like how modern pop music CDs are all recorded at pretty much the same loudness, not allowing for very quiet sections or very loud sections like you'd get at a classical music concert.
The other part of HDR as a format (HDR10) is that it has a wider color gamut. This isn't a data thing so much as it requires displays to show colors they normally can't. Old TVs never really could show a good red, the best they could do is kind of an orange, with things like blood and wine being shown dark and with a too much blue to make it look like a deeper red. Even today on a typical LCD TV, red isn't terribly red, blue doesn't go into the indigo or violet, and green is pretty mild. With a wider color gamut, an artist can ask for the usual red that normal TVs can show, but also ask for a red that would just blow your mind, and show them in the same scene.
The extra bits required to do that does imply more colors than humans can discriminate, but don't forget there needs to be room in there for the brightness levels too. It's all about brightness levels and new colors, and trust me, TVs aren't anywhere near maxing out either.