Lots of good answers already, but I’d also add, if you have the opportunity to go to a computer store like a microcenter or anywhere they have gaming monitors on demo, try one out for a few minutes, run a first person game if you can (there’s plenty of basic demos of them on the internet through WebGL), or run testufo in a browser.
It’s really hard to imagine the smoothness without experiencing it, and it’s why a lot of people say once they experienced it, they can’t unsee it.
24 is all you need to create the illusion of motion, and the brain fill the gaps, but when you control the motion, especially with a high precision mouse, it really breaks the illusion. Your brain can’t fill the gaps anymore, the motion can go anywhere at any time extremely fast. Like, even just dragging windows around on the desktop you can feel the difference. I instantly know when my 144Hz monitor isn’t running at 144. It also becomes a matter of responsiveness as the others said.
High refresh rates are also more effective at higher resolutions, because at 30fps maybe the object will need to travel 100px per frame, but at 240fps, that same object will move 25px 4 times instead. It’s probably fine when you’re watching a TV somewhat far away, but when the monitor is 32 inches and 3 feet in front of you, you notice a lot more.