Mode 2 is great for "panning" shots. When you shoot a moving subject at a slower shutter speed and follow them... a fast shutter would just "freeze" the shot (and make it look like nothing is moving). A slower shutter will result in the background blurring and implies the sense of speed or motion.
This blurs the background and the wheel spokes... but everything else looks reasonably sharp. For this example, the camera needs to be following the car as it drives by ... but you don't need to be on a tripod because mode 2 will correct for up/down shake ... but it wont fight you as you swing the camera left-to-right (mode 1 would fight you).
It's a somewhat common technique used when capturing racing. I use it when I shoot bike races.
Some newer lenses have a mode 3. Mode 3 is basically mode 1 with the exception that it is _only_ active when the shutter opens (so it wont fight you as you try to frame & focus a subject). This is because mode 1 activates the image stabilization anytime you wake-up the focusing system (whether the camera is taking a shot or not.)
