Loaded question.
60Hz monitor means the screen will refresh frames at 60x a second. If you put too many fps from the gpu, like over 300, many times the screen will literally take to long to refresh 1 frame and you'll get 2x frames loaded at the same time, this is called tearing and is most evident in motion, faster the motion more difference in object location, larger the tear. Vsync, and it's various types, locks the gpu to same frame output basically, so allows only 1 frame at a time. G-Sync does it a little different, it locks to equal frames, so if you have 50, the monitor refresh is 50, if it's 70, then the monitor refresh is 60 same as vsync.
Most of this is all done according to minimum frames, not maximum frames, in an effort to reduce stuttering and tearing since the inherent nature of games allows for large swings both ways. A slow motion explosion has far less fps swing than a fast motion explosion.