The thing is back in CRT TVs, the hertz where real. Literally. Originally a video was 30 frames per second, but that would have cause much discomfort to watch, that's why they doubled the Hz and the picture at that time was interlaced. 60 Hz TV flickered 60 times a second while the 120 Hz where doubled, hence more comfort for the eyes to the point that it was reducing epilepsy crisis in photosensitive epileptic.
Most of today's screens are LCD, meaning that the picture you're seeing is generated from pixels that are simply changing color. The back lighting being LED, which is a direct non flickering light, that is making screens very comfortable to watch.
So on a modern LCD TV the number of hertz is virtual and is not what the refreshing process used to be. When a manufacture announces that a TV is 120 Hz or 240 Hz, the processor of the TV interpolate what is going to be between frames and adds more frames. Even on a 240 Hz TV you are still watching content that is received in 60 Hz, meaning that what is going from point A (first frame) to point B (second frame) is 60 Hz, and the TV adds frames between point A and B. That is what makes the picture looking more smooth.
Of course that was very simplified and that depend on how the TV manage it. You can have 2 TVs with the same refresh rate but one will render better, as the processor better handles the picture.
If you're interested in that matter i suggest you
read this article, it's very detailed yet simple to understand.