If you want to check that what you're seeing is in HDR, pull up the "stats for nerds" option on the video in question, and it'll show you the details.
HDR stands for high dynamic range. It makes for a greater difference between light and dark parts of the picture, with more levels of granularity in between. The result should be a better image with more depth.
The Xbox Series X and Series S support HDR on streaming services like Netflix and Disney+, so YouTube is in good company. Google promised the feature on Microsoft's consoles as long ago as 2017, so it's been a long time coming.
The PS4 also supports HDR YouTube videos, but its successor, the PS5, doesn't yet. Maybe this is the motivation Sony needs.
You can read more about the Xbox update on the YouTube Help site.
Console face-off: PS5 vs Xbox Series X: which is better?
Read our full Xbox Series X review
And our Xbox Series S review
Here's our PS5 review