A 60hz monitor refreshes the screen 60 times per second. Therefore, a 60hz monitor is only capable of outputting 60fps. It can still feel smoother to play at a higher framerate than your monitor can display however, because input lag with your mouse will be reduced. You might also start to see tearing though, which happens when your videocard is rendering frames faster than your monitor can display them.
-Straight from the inter web!