HDR stands for high dynamic range. It means you can have detail in shadows and highlights without losing detail in the middle.
At the end of the day, it's just how your computer or console talks to the display. It doesn't change what your display is capable of. It can't magically make colors more vibrant, for example. What it does instead, with a quality display, is allow you to make specific colors more vibrant while keeping their detail, without losing it elsewhere. It should usually be subtle, except in specific showcases designed to push the edges of what HDR can do.
It also doesn't make a mediocre display not mediocre. If it can't accurately present the whole range, receiving it doesn't help a lot.
Edit: oh, didn't realize this is the steam deck sub. You probably can get actual feedback on the quality of the display, then. But it will still really only make a difference to quality if the developers made a specific effort to utilize it. Realistically, that's mostly on high quality lighting the steam deck can't really do.