Each manufacturer has a different name for this stabilizer, for example Nikon with VR (Vibration Reduction), Canon with IS (Image Stabilization), or Sony with SSS (Super Steady Shoot). Technically there are two ways to reduce vibration.
(1) Stabilizer on the lens (optical), applied by Nikon, Canon, Panasonic
(2) Stabilizer mounted on the sensor (body), are implemented by Sony, Olympus, Pentax
Whichever system you choose, the existence of image stabilizer will be very useful because it is effective reduce vibration up to 2 or 3 f-stops lower. The following example of the effectiveness of damping you can see in the picture below:
But that does not mean this feature may replace a tripod. Its effectiveness is based on my observations is 2-3 f-stops. So if you are able to hold the camera without vibration at shutter speed 1 / 30 s with no image stabilizer, means with the help of this feature, you will be able to shoot with a sharp in 1 / 15 or 1 / 8 s. But if you use a speed of 1 s, of course, will remain blurry image due to vibration.
