Why is screen refresh rate considered important in gaming?

Let's start with the easy one.

Can the human eye actually tell the difference between 60hz and 144hz?

Yes. It's one of these "you gotta see it for yourself" thing. 144hz looks crazy smooth. Even just moving the cursor around the screen is impressive at first.

why is refresh rate considered important beyond 60hz?

Well in the context of games, assuming your PC is powerful enough, higher refresh rate means you can see more frames per seconds. If you have any experience with video games, you'll easily understand that higher FPS = smoother video, more precision and better responsiveness. Just keep in mind "maxing out" your 144hz display means your PC needs to be able to render 144 FPS. A game locked at 30FPS won't be much different on a 144hz display.

It's really just the same arguments as 60fps vs 30fps, except that in this case we're talking about the physical limit of the screen and not the virtual FPS your PC can compute. You could have a game running at 60FPs on your 144hz display, but you can have more.

Why it matters to me[...]

144hz doesn't inherently improve the image quality. If 1080p looks blurry to you, 144hz won't help. A blurry still image is still blurry at 144hz. What do you want to use this laptop for? Casual games, netflix, browsing? Disregard 144hz and go for 4k. Fast-paced games where you want every advantages you can have? Don't buy a laptop Do consider 144hz.

Let me just focus on this one: why is refresh rate considered important beyond 60hz?

A framerate of around 24hz suffices in theory to see a series of frames as a continuous signal. At that rate we perceive a series of "slides" not as such, but as a movie. You won't see individual frames beyond that.

But that's not the end of the story.

Even if you don't see individual frames, it may not be enough for an eye to successfully track fast-moving objects. Even in films, in a high-action sequence with a lot of movement, 24fps may not be enough.

Consider an FPS game with a rocket moving right in front of the viewer, from left to right. It will appear only for a fraction of a second. If you are playing at 30Hz or 60Hz, at each frame the rocket will be rendered at a very different location on the screen. When that happens, the brain may still have problems to identify that it is indeed the same object moving, and not just a sequence of different objects with some unspecified velocity.

The above issue intensifies if you have a multiple objects on your screen and your brain needs to track frame-to-frame all of them without mixing them up.

So, how much is enough?

It really depends on your brain and on the game you are playing. How many fast-moving objects are there on your screen? How accurate you need to be in the game?

First Person Shooters are probably the most demanding in that aspect. Not only you need to track your opponents with an eye, you also want to actively track them with your mouse (or whatever controller you have). Moreover, as you rotate your character, the whole world - and not just the moving objects - are moving on your screen at a high rate. When that happens, if you are at low framerates, your brain may be totally lost causing you dizziness...

Especially, if you are a professional in the FPS gaming, where aiming comes automatically to you without any conscious thought, the difference between 60Hz, 90Hz, 144Hz and even 240Hz may be a major difference! So, if a gamer tells you that he sees a difference, it's probably not because he is an elitist, but because it has a real impact on his performance in the game. Even if that 'see' is not about seeing individual frames.

Other games with a virtual world perceived from first- or third- person view, but without precise aiming, can still improve from higher framerates, but it is not that cruical.

But then, there is a wide array of games, e.g. RTS games with top-down view. For those I don't think you need anything above 60Hz. Your whole screen does not changes as much and you don't need to aim at fast-moving things. Usually.

In addition to the other posts, 144hz has lower input lag than 60hz. See this video to understand why.

I used to think all the concern about input lag was hogwash, but then I played Rocket League on 144hz and it felt so much more responsive. After a few months of that I tried switching back to 60hz, and I consistently missed every hit because of the huge difference in timings.