HDR is short for “High Dynamic Range,” and it’s the principal feature that sets many 4K displays and monitors apart. It’s a collection of new standards for displaying color and brightness information that allows the display to dynamically adjust its brightness at a very precise level, allowing for more accurate and vibrant displays.
Its current big challenge is that it’s going through a format war just like the old Beta/VHS or HD-DVD/Blu-Ray eras, with competing standards all scrambling to get the most support in displays, game consoles, movies, and software.
You can read about some of the different formats here.
High-dynamic-range video - Wikipedia
High-dynamic-range video (HDR video) describes video having a dynamic range greater than that of standard-dynamic-range…
Unlike 4K resolution itself, which can be tough to discern massive differences in depending on display distance and other factors, HDR is immediately obvious because it provides a dramatic amount of additional brightness and color detail. You can see this for yourself if you have an electronics store nearby. Dolby also has a tool that will simulate the differences on a standard display right here, if you scroll down a little bit.