The downvotes are because of a common irritating myth that you don't need >60fps because of 60hz. The two are not correlated; while it's true a monitor will begin ignoring frames sent to it beyond its refresh rate, the fps still affects the polling rate of the game itself... referred to as frame latency. Read more about it here.

Exact 60fps is a frame latency of ~17ms between frames being sent to the monitor, regardless of what the monitor is doing. That means with a 60hz monitor, the frame you're seeing could be up to 17ms old by the time it appears on the display (plus whatever monitor latency there might be... 2ms or whatever). At 300fps, you're looking at ~3ms of frame latency. Most gamers will simply says it looks/feels much "smoother".

If you're ever skeptical, watch a full benchmark run of something like 3dmark with the fps display on.You can very clearly notice the difference between the ~60fps scenes and the ~300fps scenes, regardless what the refresh rate of your monitor is.