The 5D MkII does not support this natively, as far as the manual says. You possibly have Magic Lantern installed. The easiest way to check this is to press the trashcan button while in Live View mode.
If a menu pops up, you have Magic Lantern installed. The corresponding feature is called trap focus. From the documentation:
Takes a picture when the subject comes into focus.
Hold AF button you need to hold the autofocus button (half-shutter, * or AF-ON, depending on your settings).
Continuous you don't need to hold any button; ML will hold the half-shutter pressed for you. This will also block most buttons; press the shutter halfway to unlock them for two seconds.
Outside LiveView, it only works with lenses with chip. In LiveView it only works for photos, and it will take a picture when the focus indicator has (almost) maximum value on the focus graph. You may have to turn the lens back and forth a few times in order to let ML compute the correct focus scaling factor for the current scene. If you move from a high-contrast scene to a low-contrast one, you will also have to wait a bit until the high-contrast data disappears from the focus graph. Press SET to temporarily disable automatic scaling of focus magnitude.
The setting can be found in the Focus tab of Magic Lantern:
(disclaimer: I do not have any Canon hardware nor have I had the chance to test any Canon hardware yet. This answer is based solely upon my perusal of the 5D mkii manual and Magic Lantern manual)