With refresh rates like that, you must be talking about LED billboards.

These are different from consumer monitors, which mostly use constant LED backlights and a liquid crystal layer to determine color.

An LED bilboard is going to have a fuckton of singular LEDs - each of which can emit exactly one color - arranged in groups to form full pixels capable of displaying many colors. There is no extra LCD layer between your eyes and the billboard LEDs.

The reason for the high refresh rates is because each led must be extinguished and and relit to redraw the image, and the eye is very good at picking up this strobe effect.

The difference vs. a consumer display is that the backlight in a typical monitor is constant. Refreshes the screen involves sending updated instructions to the LCD layer, twisting the crystals and possibly changing the color they allow through.

To make a crude concrete example:

Imagine I am shining a white flashlight in your face. In front of the flashlight I put a colored piece of plastic so the light hitting you is colored. Then I change the plastic to one with a (slightly) different color. I do this 120 times per second. That is a typical consumer display.

Now imagine I am shining a colored flashlight directly in your face. Then I turn it off and grab a flashlight of a different color and shine it in your face. Imagine I do that 120 times per second. That is an LED billboard.

Which do you think is more likely to give you a headache?

One final complication - the brightness of the LEDs is variable over time, they received a modulated signal rather than a steady voltage, so at lower refresh rates there will be a noticeable ripple across the image, similar to how early CRT screens could look.

Increasing the refresh rate hides a lot of these problems.