The refresh rate of the monitor is also connected to FPS in games because the game can only draw a new frame as the monitor also begins to draw a new frame. If your monitor is only running at 60 Hz, it would then be impossible for it to display over 60 FPS, even if your computer were generating them. In fact, you would often be seeing far less than 60 FPS as the computer can only draw a new frame when the monitor is also beginning to draw a new frame. If another frame is ready to be drawn and the monitor is still in the process of drawing the last, this new frame is lost, and so would any others that were created during the interval of drawing that frame. This can sometimes result in a significant number of dropped frames.
To get around this limitation, gamers often disable a feature called "v-sync" or "vertical sync" in their video drivers (the function is usually buried several layers deep in their computer's display properties). By turning v-sync off, the monitor is then effectively fed partial frames, as it begins drawing the latest frame available without waiting for a new cycle to "sync." But as only partial frames are drawn, this can sometimes result in "tearing" (this is more noticeable in games that use DirectX rather than those which use OpenGl, as the latter actually does not contain a v-sync function and handles the feature differently) where "seams" appear when there is fast motion in games--though this is encountered far less with modern video cards than it was in the past as it is more evident in displays with lower refresh rates (60-72 HZ.)..