Vertical sync (Vsync)
Vertical synchronization is an option used to prevent screen tearing. Screen tearing is a graphical glitch which is perceived as straight horizontal lines across the monitor or as if the whole picture is stitched together by two or more separate pictures. This problem exists because the monitor and the graphics adapter normally works independently, so new frames may not be fully drawn when the monitor display them. V-sync makes the graphics adapter wait for the monitor to signal it's ready for the next frame to ensure all displayed frames are always fully drawn. This has the positive side effect of limiting the amount of frames per second the computer has to draw to the monitor refresh rate (the amount of frames per second the monitor is able to display) which saves resources. Unfortunately V-sync can also increase input lag.
- Eliminates tearing by waiting for the monitor to signal it's ready for the next frame.
- Lower power consumption (and therefore heat and noise) by limiting FPS to what the monitor is able to display.
- Introduce extra input lag. Commonly experienced as "mouse lag".
- May decrease performance if FPS falls below the monitor refresh rate.
- Only available in fullscreen exclusive mode (a borderless fullscreen window does not qualify).
- Not to be used when benchmarking since the FPS will be capped at the monitors refresh rate.
 So what's the best option?
There is none and results will vary between different games, systems and people. If you're bothered by tearing or want the best visual quality, enable V-sync. If you're bothered by input lag or have performance problems, disable V-sync. If you're playing first-person shooters competitively, always disable.
Note that V-sync is not a FPS limit. If you only want to limit FPS drawn, for example to minimize heat and fan noise, but is not bothered by tearing and don't want to risk input lag, simply limit your FPS to that of your monitors refresh rate or close to it. An FPS limit is often an option available as an in-game console command or similar.