Consider some time in between two vsyncs. Suppose the first display buffer is being used to display the current image, and suppose the game was really fast and computed and rendered the next image to the second display buffer and the next one after that to the third display buffer. That is the rendering to the second and third display buffer happens so fast that it occurs before the next vsync.

Suppose input from the user comes in now. What you would like is for the results of the input to show up on the next vsync or (probably more typical) the vsync after that. However, with the third display buffer already rendered the input can only effect the image after that. Meaning the input will only take effect at best 3 vsyncs later.

I wish i had an image to show the exact timings of what I mean.