Honestly I'm more on the sensitive side. A few stutters and I feel a need to change settings on PC, or just don't like it.Frames per second. Basically it's how smoothly the game can render individual frames. Personally I don't really care for them that much, but there's people who apparently take them pretty seriously
I've also noticed that I just notice them more than other people. Like, in my opinion Pokemon Mystery Dungeon: Rescue Team DX does not run well at all. I've noticed stuttering even in in-engine scripted scenes, and there is even input lag I notice. But I haven't seen anyone else find it. Even when I show people a video, they usually have to slow down the video to see it.
I'm not sure why I am this way. I didn't even grow up with snobby stuff or whatever, I grew up on Nintendo systems. Getting into PC gaming (for the record I have a low end one, can barely play new gen games) certainly did play a part, but also the eyes can definitely adapt.
For certain genres I think it 100% matters though. Hardcore platformers, rhythm games, fighting games, etc. IMO need 60fps minimum, because the lower FPS also makes it harder to get out inputs as soon as possible. I will never play Super Mario 3D World Bowser's Fury in handheld mode because it cuts the framerate in half, and it just feels less responsive and IMO looks kinda bad.