LCDs do have refresh rates but they work slightly differently to CRTs.
On a CRT, only one 'pixel' is illuminated at one time - the electron beam is swept across the screen left-to-right, row-by-row. The pixel illuminated corresponds to the signal being send from the computer at that precise time, and the brightness and colour of that pixel depends on that signal.
A refresh rate of 60 Hz, means that the beam makes 60 sweeps of the whole screen per second. The eye has a slow response time (equivalent to about 30 Hz), so it blurs out this sharp flickering - but nevertheless a high refresh rate is needed to reduce the flicker so that it is not actually noticable (about 85 - 100 Hz).
On an LCD, every pixel remains illuminated continuously - there is no flicker. However, the information is still being pumped pixel by pixel from the PC. When a pixel receives a signal that is different from what it is currently displaying - it starts changing colour. This process of changing colour takes some time. This is the LCD response time.
So, if your LCD is running at a refresh rate of 60Hz - it will receive a set of instructions every 1/60th of a second. However, if the response time were 25 ms, then it would mean that a colour change instruction would take 1/40 of a second to complete.