Refresh rate can be important in some venues, especially those with broadcast events
Refresh rate can be a confusing specification, and is often mixed up with frame rate. But frame rate is generally a property of the incoming source material, rather than the display. So a video will generally have a frame rate of 24 or 30 frames per second. Anything above 15 frames per second is perceived as smooth to the human eye.
Refresh rate, on the other hand, is the rate at which the LEDs in a display are signaled to update their color. This number is in general much higher than the frame rate of the incoming video. So multiple screen refreshes will generally repeat the same frame to match the frame rate to the refresh rate.
For example if you have a 24fps video playing on a 120Hz refresh screen, the processor will repeat each frame 5 times to the screen to make the 24 frames take up one full second on the screen.
This is an area where the processor comes into play, as the higher the quality of the screen and the higher the refresh rate, the more work a processor must be capable of to refresh the screen.
LED screens can now refresh as fast as nearly 10,000 Hz, but people have used computer monitors and CRT screens with 60Hz refresh rates for decades. The refresh rate, then, is a lower-tier issue, probably not something to put extra money into, but more a number that might tip the scales toward one proposal over another.
One consideration is if you have a screen that might appear in video or film often. In order to produce flicker-free images when being recorded, a display should have a refresh rate somewhere around 1000 Hz or above. Beyond that, any modern display will appear smooth to the audience.