The only reason to buy a 120Hz monitor is if you are planning to use for 3D gaming. Otherwise, there really is no advantage to it seeing as how many games render graphics at a rate much below 120Hz.
That's plain wrong.
Games don't render anything and GPUs don't render in Hertz intervals, they render when it's finished being processed as fast as physically possible. It's the the monitor that periodically refreshes its display (as it has to, unless you'd only see a black monitor), in intervals measured with Hertz.
And as I've said, the difference is significant. Double the frame refreshrate means you see double the frames. So if you have a GPU that can render a game at 120 fps, with a 60Hz monitor you only see half of those.
You can compare it with animated comics. Draw a motion comic in crude successive pictures and you see motion. Draw the same visual with more standalone pictures and speed up the animation and you have a smoother visual because the differences between each single frame is less.
A 120Hz monitor won't make a picture more pretty, but it will improve the visual quality of motion significantly.