Is the refresh rate that we set using monitor properties ( in say ubuntu) the actual number of times X will refresh the screen in 1 second ? Or is it just some configuration of the hardware and has nothing to do with the frame rate ( ?) of X server ?
It is hardware frame rate configuration; how that maps to what software does depends on the video driver and whatever other software you're working with. In particular, X11 itself does not actively refresh in the way you seem to be thinking of. Software frame updates of the sort you are talking about typically are controlled by higher layers than X11 or the video driver; check the documentation for whatever video library or framework you are using.