HDR is one of the latest standards for digital content and monitor standards, aimed at improving color reproduction and range.
it has nothing to do with a monitor's resolution (e.g. 1080p, 4k, etc), panel (TN, LED, OLED, etc), or the "HDR" in your phone camera settings right now.
the biggest standard right now is HDR10. some companies have built "HDR capable" products for now, that don't support the "Full HDR" specs. to really benefit from HDR, you'll need native HDR content + equipment that fully supports its specs (this includes TV / monitor, cables, output device like TV box or computer graphics card, etc) note: a HDR TVs' spec is not the same as HDR computer monitor's spec, even if you find a TV and monitor that both support HDR10.
then, there's also the recent addition of Dolby Vision etc, which adds yet more standards into the mix. most reviews tend to note that HDR is still very new, so you need to be careful. if you can afford it, Dolby Vision usually gets better reviews for color depth and range afaik.