Some of what matto17sec said is correct, though the vsync part was not. I'll try to explain.
Your video card renders frames independently from the monitor if v-sync is off. It can generating as many as it wants. However, the monitors only updates at its refresh rate, which is usually 60hz. However, if your video card is generating 120FPS, you will notice a difference from 60 FPS.
What happens is you get partial images displayed to the monitor. As the monitor updates the image, if the frame buffer changes midway through the update, the part of the update which hasn't been completed, will be completed with the new frame. This causes tearing, but it also improve responsiveness, because you do see a new update from an action you just did. This update, may only be on part of the screen, but it is noticeable. The bad part is you get what looks like lines through the screen, where the older image and newer images change.
With vsync on, the video card cannot write to the frame buffer until the monitor is done updating its image, preventing partial images from appearing. Without triple buffering, this causes the GPU to stop doing anything until that time. With triple buffering, it'll wait with one buffer, but start making a new frame with another, but it still will not generating more frames than your monitor can display.