Yea I get what you mean, I'm a beginner in computer programming and want to be a video game programmer, its just that I've never encountered that option before. Thanks for the information.
More specifically, this option kind of has deep roots in old CRT displays. There was a period of refresh where the cathode ray would go from the bottom corner to the top corner to start drawing the screen again. The period this gun traveled was commonly known as "vertical blank" or "vblank"... at least that's my memory.
Since forever it's been possible to synchronize your graphics code to this vertical retrace so that you could do work between screen refreshed. This would also prevent you from doing strange things like modifying graphics memory while the screen was refreshing leaving partially rendered images.
Well, that's a history lesson anyway.
Really, your monitor can only refresh at a fixed frequency... generally 60 hz. It doesn't matter how fast the game is rendering because you will only ever see 60 frames per second. So when I run Mythruna and I get 240 FPS on some area, I'm still only seeing 60 frames per second. The game is just rendering an extra 180 frames that I never see. In fact, in full screen it's sometimes still possible to see artifacts called "tearing" if you turn too fast while at a frame rate significantly higher than your monitor's refresh... you will end up seeing part of two frames. In other words, the image looks torn with the bottom part skewed from the top part.
Vsync forces the game to wait until one frame is drawn and dispatched before continuing. (Actually, I believe it's actually that before dispatching the next frame it makes sure the previous one has completed... since then the game gets to still render the next frame while the previous one is displayed... but I digress). You will never see more than the refresh rate as FPS in this case and the game can spend time doing other things like physics and AI and generally being nicer to your system. It isn't wasting time drawing frames nothing will see.
The only down side is that it can exaggerate performance problems. For example, if a frame consistently takes just slightly longer than 1/60th of a second then instead of getting 57 or 58 FPS, you might drop a full multiple down to 45 FPS or 30 FPS (depending on how steady the delay is).
When running/playing the game, vsync is really the "right" way. Leaving it off is a good way to test performance (which is why I do it) or to brag about your system specs (Dudez, I totally got 600 FPS in full screen!!!)... but it's making the whole system work harder for no good reason.