On video monitors, there are actually two refresh rates, but you normally only hear about one. The horizontal refresh rate is the inverse of the amount of time it takes to draw a single line on the screen:

A typical monitor has a 31.5 KHz maximum horizintal 
frequency, as determined by a crystal installed on the 

  31.5KHz = 31500Hz

     -------  =  0.000031746 seconds

So, in 0.000031746 seconds, it draws a single line across the screen. Most people have heard about the vertical refresh rate, because these numbers are touted by the sales advertising.

To determine the vertical refresh rate:

    Horizontal Frequency (In Hertz)
  -----------------------------------  = Vertical Refresh
      The number of rows (lines)

Since a typical SVGA monitor can display 640 x 480:

              -------   =   72Hz

Continuing using similar numbers:

 A monitor running 800 x 600  =  72Hz (rounded)
 A monitor with 1024 x 768    =  70Hz

Normally, a higher refresh rate gives you better picture quality and less flicker. You do not want to have a 60Hz vertical refresh rate or less, especially since flourescent lights also operate at 60Hz, which gives pronounced flicker and an almost stop-motion scan line that progresses down your screen. In countries that have a 50Hz electrical system, you don't have to worry as much, since I personally don't know of any sub-60Hz monitor refresh rates.