Monitor Hz is how fequently a picture is drawn on the monitor. People can only see a given number of images in a second.
Monitors show brief points of light that quickly fade to black. This happens repeatedly - so fast that your mind blurs the light and ignores the black. If a monitor displayed at 1 Hz, you would actually see a picture for a fraction of a second and black for the rest of the second. Basically it would look like it was turning on and off at a frequency of 1 Hz.
If that 1 Hz monitor was set to 2 Hz, you'd see two images each second and black in between. Imagine that frequency is slowly turned higher and higher. People's eyes/brain have a limit to how fast it can see images. Eventually your eyes/mind will blur the light together and ignore the black - forming an image that APPEARS to be on all the time.
The exact frequency where your eyes/mind can no longer see the black varies from person to person. For example: Flourescent lights turn on and off at 60 Hz (in America, it is less in some other regions), and some people can actually see it turn on/off in a flicker that gives them migranes - while most other people look at a flourescent light and see constant light.
Obviously if your monitor is at 60 Hz and you get headaches from a flourescent light, then you will also get headaches from a monitor flickering on/off at 60 Hz. For other people it makes no difference. That is the reason that monitors have adjustable refresh rates - since different people are different. If it bothers your eyes, turn it up a bit.
Note: going too high can cause another problem. Any multiple of your limit will also cause problems. So if you have problems at 60 Hz, you'd also have problems at 120 Hz. So I don't argue to always set it as high as possible - instead set it as high as is needed to avoid eye problems and headaches.