Tearing is what happens when the game is redrawing the screen faster than your monitor can refresh it. What happens is that you start getting instances where the image breaks in the middle of it as its showing two different frames at once.
Wikipedia has a good example / explanation of whats happening with it.
http://en.wikipedia.org/wiki/Screen_tearing
vsync forces it to only redraw at the max speed the monitor can handle. (Most standard LCD's is 60Hz / FPS)

And +1 for running XIV with crossfire. I have dual 5750's, when I built my machine it was the best performance per $ in my price range. A single 5750 however is not THAT great on its own and running XIV in windowed mode really slows down. Full screen performance is MUCH better when both cards can be fully utilized.

As for them having to redo parts of the graphics engine, this should have never been the case in the first place. Its a bug, and I will continue to label it as such till it gets fixed.