They are 'camera shake reduction' systems: IS - Image Stabilisation (Canon), VR - Vibration Reduction (Nikon), OS - Optical Stabilisation (Sigma), and VC - Vibration Contol (Tamron). It's brilliant technology and works very well.
When you hold a camera, there is always some movement known as camera-shake that can blur the image. This increases with focal length, and the rule of thumb is that most people can successfully achieve sharp results when the focal length (on a full-frame camera) equals the shutter speed - say 1/500sec with a 500mm lens.
Shake reduction systems detect the shaking and shift lens elements extremely rapidly to correct it, so the image stays sharp. There are also in-camera shake reduction systems that shift the sensor to compensate.
Both methods are extremely effective and a claimed 3-stops of improvement would mean that in the example above 1/500sec could be reduced to 1/60sec and still get a sharp result (1/250sec being one stop, 1/125sec two stops, 1/60sec three stops). Obviously very useful in lower light, or when you want a high f/number that would also push the shutter speed down.
However, shake reduction systems can do nothing to reduce blur from subject movement. Arguably, this feature is less useful on shorter focal length lenses like wide-angles and also with low f/number lenses like the 50/1.8 mentioned above. It's much less commonly found on these kinds of lenses.
