Gsync basically allows for a dynamic refresh rate that matches the output from your graphic card. Before gysnc existed, there two main modes vsync and not vsync.So if we turned vysnc off, we would get whats called tearing that is basically saying graphics on your screen might contain part of the last frame and part of current frame. Infact even in worst condition, you can get multiple tears across the screen so you're seeing 3 or more separate frames on your screen with objects in different positions.With vysnc on you will not see any tearing, however , in order to compensate the screen will simply draw two of the same frames whenever your frame rate dips below your refresh rate of the monitor. So vysnc on means you have 60 hz display you will run exactly at 60 fps unless your graphic cards lets say dips to 59fps just even once , it will draw 2 frames just for that one frame and that is stutter. The other problem with vysnc is the lag (causes input lag). Gsync updates the screen exactly when the frame is finished and ready to be up by the graphics card whether that is 55 or 59fps.. It eliminates all the problem associated with vsync : matches fps, no lag and no stutter.
Triple buffering: Basically, it lets your hardware pre-render the frames if your hardware isn't good enough to render in real time when vsync is enabled.
Adaptive Vsync: Basically, if its enabled the driver(s) will enable/disable v-sync based on your frame rates.
There is no relationship between response time and screen tearing.