Here's the gist of it as far as gaming goes, what your eyes can see, and what your brain can register.
Your eyes can only "see" 60 Hz, that's the mechanical cap the good Lord (or whoever your chosen deity is) put into the human body. However, your brain can accept far more information than that, so 144 Hz and beyond is visible to the brain. So, even though you can't actually "see" it, your brain knows it's there, and you are able process it.
The difference it makes to gaming is that you can now react faster to the perception without waiting for the sight ... you get what I mean here?
In competitive games, milliseconds mean life or death.
I play World of Tanks. The bonus to me to run the game on 144 Hz monitors (yes, I said monitors) is that it has improved my scores tremendously across the board. I can see and shoot people well before they can see or shoot me. I never have screen lag that causes me to shoot behind people.
My son plays Fortnite. The 144 Hz monitor he plays on means he is shooting people before they even see him. He quite regularly now finishes in the top 5 of his matches.
As for just plain looks, regardless of the game you are playing, 144 Hz is simply way more smoother.
In short, the more Hz's you can effectively display over 60, the better your game play and experience will be. After that, the fact that you're not a pro player is on you and not your equipment ... LOL
The ultimate, if you can afford it, is a 4k, 144 Hz, 27" monitor. They were on sale last week for $2,199.00 CDN ... LOL
As a side note ... a couple weeks ago Newegg.ca had Asus Rog RTX2080Ti's for sale cheaper than any GTX1080Ti they had. Seemed kind of odd, but I didn't argue. I bought an RTX2080Ti ... LOL. Of course I didn't get to keep it ... it's in my son's machine. Fortnite never looked, or played, so good.