Vsync synchronizes your frame rates to your monitor's refresh rate. If your monitor refresh is set to 60, your fps will be capped at 60. Btw, 60 is default normally. Most modern monitors can do 85hz at popular resolutions (i.e. 1024x768). There are many now that can do better.
You mostly want it off if you are benchmarking or testing to see how well the card itself responds to changes. When you see benchmark tests on Tom's Hardware, or Anandtech, or whatever, they have Vsync off when they are showing you those 100-200 fps marks.
So if it gets better frame rates with vsync off, why turn it on? For a few reasons.
1) You cant see those frame rates anyway. Whatever your monitor's refresh rate is, thats all the monitor is going to show. Period. Even if your video card is pumping out a mighty 500 frames per second, if your monitor's refresh is set at 60hz, you will never physically see more than 60 frames per second. Fps is always going to be hardware limited by your refresh rate on your monitor, no matter how good your video card is.
So ok, I cant see the frame rates my uber card is putting out, so why cant I just leave vsync off and make myself feel good with those big fps numbers?
2) When Vsync keeps the card's fps in line with the refresh rate, it's also making sure that the output of the card matches what the CPU can accomplish. While your card is pumping out those mighty 500 fps, the CPU is lagging behind. It's trying to take care of the textures and swapping info between system RAM and video RAM, reading info off the HD, managing all the devices on the system bus, AND trying to communicate with the AH server to update your FE. The result? While your video card has displayed 500 frames, your CPU only processed 250. What happens is, your video card stops showing frames until the CPU catches up. Or you get "tearing" in the video. People are going to argue that modern computers and CPUs are capable of keeping up, so tearing and freezes are an issue of the past. I disagree. Especially with a game that hits the CPU as hard as Aces High.
You do what you like. I'd rather have smooth 35-80 fps than risk a big screen freeze at a really critical moment. Had it happen. Sucked.