"I must have slept, what is HDR?"
High Dynamic Range.
Along with the other responses, in this particular context(*) however, it means the difference in brightness level between Full Off (black), and Full On (white) of the display technology - the wider the difference, the better.
Raw screen brightness is only half the equation, how black the blacks are, also factor in. It's kinda like the LCD vs Plasma debate all over again. Plasma has a darker black, but LCD overall is better in other areas. OLED has the technogical potential of doing better.
(*) HDR in the context of photography is a "different" thing. In Real Life(TM), dynamic range is just extraordinary, in space it's as wide as the physics can make it, on earth, atmosphere tends to make it fall short a bit, but it's still Holy Crap(TM) wide. Even though the human eye can't compete - it still rates as bloody good. Present day technology however, be it Film, CMOS, CCD, Plasma, LCD, OLED, etc, are just terribly narrow in comparison.
To address this, HDR photography involves taking a range of photos of different brightness of the same scene, and picking the best of the darks, middles and brights, and manipulating the images in software to make it narrower overall.
It does NOT magically give you a higher dynamic range, it just takes Real Life, and makes it fit within today's technology, so it looks nice.
So while HDR in future technology would most certainly be a good thing, I think we're a long, long way away.