Also referred to as HRR, high refresh rates generally mean 120Hz and over. As you probably know, gaming monitors now routinely do 144Hz and even 240Hz, albeit in lower resolutions and with toned down graphics settings. On PC, 60Hz has been the minimum “acceptable” framerate for a long time, and now consoles have also caught up. In short, 60 frames per second regardless of resolution is considered the baseline for enjoyable gaming.
Without getting into lengthy explanations, framerate helps determine gaming enjoyment because video games by their nature need to be responsive and feel smooth when you interact with them. Lower frame rates cause everything to seem sluggish and unresponsive, and once you experience 60Hz or more, going back to the old 30Hz standard that dominated consoles between 2005 and 2020 is very jarring.
Current generation consoles have so much power available that even the least motivated developers can easily pull off 60Hz, and that benefits every game genre. First person shooters and racers focus on response and reflexes more than story-driven exploration titles or role playing games, and therefore benefit greatly from uncapped frame rates. If you enjoy FPS titles and racing games, the smoothness of 120Hz and over cannot be understated, and genuinely helps not just in enjoying the game more, but performing better if in a competitive mode.