It seems like new technology keeps popping up for the home TV, and we keep being encouraged to buy a new set to "keep up". Personally, we still have a 720p flat screen as our main TV in our home, so you can probably tell how little I try to keep up....
Anyway, HDR is the latest thing that you probably see in ads for new TV sets. "High Dynamic Range" (HDR) refers to the ability of these TVs to better display contrast and scales of brightness in the TV image, and this leads to a very pleasing effect for most viewers.
If you put two TVs side by side, and one has a better contrast ratio and more accurate color, and the other just has higher resolution (more pixels), the one with greater contrast ratio will be picked by pretty much every viewer. It will look more natural, "pop" more, and just seem more "real," despite having lower resolution. In other words, a 1080p resolution TV with excellent contrast and color beats a 4K resolution TV with average contrast and color every time.
In photography, HDR usually indicates something slightly different, in that it usually refers to those photos that "play" with contrast and color to often produce an almost "dream like" effect. See here for some examples.
Read more about both kinds of HDR at CNET here.HDR for cameras is a capture process. This is where multiple photos with different exposures are combined to create an effect that can look more (or less) realistic than a single exposure could.