It’s mostly noticeable when you play fast paced games where you might for example turn your field of view 180 degrees in a fracture of a second to look behind you, or when you’re for example being chased or moving into hostile territory you will do a lot of rapid camera movement to keep a look out. With low fps, the screen turns into a blurry mess during those moments, preventing you from keeping your eyes on important visual information and requiring you to get your bearings again each time you stop to look at something. The higher the fps is the more snappy and crisp are these situations and the easier it is to keep your eyes on something during movement or to execute a precise maneuver.
Granted, for slower paced games a lower fps max be just fine, but anything hectic will be less enjoyable.