YouTube notes that, "HDR videos have higher contrast, revealing precise, detailed shadows and stunning highlights with more clarity than ever. Support for wide color gamut means colors are more vibrant. Simply put, HDR unlocks the most spectacular image quality we've ever streamed."
Tapping the three dots at the top right of any video will bring up a menu where you can select the quality. You'll notice 'HDR' listed after the resolution where it's available.
You can download YouTube from the App Store for free. A simple search for HDR will bring up plenty of videos to try out!