how important image stabilization is in digital camera
In simple words for our understanding Image stabilization increases the stability of an image.
image stabilization allow the use of shutter speeds three to four stops slower (exposures 8–16 times longer)
Image stabilization is designed for and is capable of reducing blur that results from normal, minute shaking of a lens due to hand-held shooting. Some lenses also includes a secondary panning mode or dual image stabilization mode that is more aggressive “active mode”.
Note: image stabilization does not prevent motion blur (extreme movements of the camera).