While technically the human eye wont notice if you show something at 30FPS or 300FPS if the images are done properly, this doesnt quite apply to games due to the nature in which the images are displayed. In movies when something is moving across the screen its location gets blurred between frames, this helps convince your eyes that it is moving and it seems a bit more realistic. In games however, items do not blur from one location to another, they have a specific location in each frame and items that are in motion are generally not rendered with a blur so higher FPS help smooth this out as your eyes are blurring the frames together anyway, it just makes each item jump less between frames so it seems smoother and more realistic, this is why some games come with an option to enable motion blur.
Most people are only affected once it drops below about 40FPS which is why tom's uses that as their "playable" threshhold.