Ok, each frame that's rendered is drawn into the frame-buffer (the memory in the video hardware that stores the data that represents the frame that's currently being displayed) line by line from the top down, replacing the previous frame as it goes. When the display wants to display the next frame, it reads what's in the frame buffer and displays it. When the display and the frame buffer are out of sync you'll sometimes see the display reading the frame from the buffer while the video hardware isn't quite finished writing the frame. So, you'll see part of the previous frame and part of the next frame at the same time, and they might not line up correctly. That's tearing.
Displays have a refresh rate typically measured in Hertz (Hz). This tells you how often the display wants to read a frame from the frame buffer. Most LCDs have a refresh rate of 60Hz, which means they refresh 60 times per second. If your video hardware is producing 110 frames per second there's a good chance that, at some point, the display is going to read from the frame buffer at a time when there are partial frames being displayed.
Vertical sync causes the software to wait to start writing the next frame to the frame buffer until the display is finished displaying the previous frame. In the example above this won't work. We can't synchronize something refreshing 110 times per second with something refreshing 60 times per second. Now, we could sync a video source refreshing 120 times per second with a display refreshing 60 times per second, but it would be kinda pointless because you'd only actually see half of the frames being rendered. It makes more sense to limit the video source to 60 frames per second so we render exactly the number of frames we're going to see.
Now, the 360 is locked at 30 frames per second, so a 60Hz display is going to display each rendered frame for exactly two refresh cycles. Since these can sync up (1 frame per two refresh cycles divides up nice and neat) we shouldn't see any tearing. If for some reason the 360 can't maintain the 30 frames per second it has to limit its rendering speed all the way down to 20 or 15 frames per second in order to stay synchronized with the display (because these numbers divide evenly into 60). 20 or 15 frames per second is not fun in a video game, so it's probably designed to stop trying to vertical sync rather than slow the framerate to a crawl. What we're probably seeing is the 360 occasionally dropping below 30 fps. If the 360's framerate can't be comfortably limited to something that divides evenly into the display's refresh rate (and it can't if the rendering framerate drops below 30 frames per second) you're going to see tearing.
Clear as mud?
TLDRLong story short, this might not be something that can be turned on and off. If the 360 isn't maintaining 30fps the only option to avoid tearing is to drop it down to slide-show city. That's something that you don't want (15-20 fps is slooooow), so it's probably designed to go ahead and show you the tearing rather try to sync below 30fps.
I can't remember if the PC had a vsync option, but yeah screen tearing is a major headache.
On the PC you can force v-sync to be on in the video driver, so you can turn it on even if the game doesn't have an option for it.