Image stabilizing is simply a technique to reduce the blurring effects camera shake can have on an image. The image stabilizing is done automatically by the camera or lens.
Canon and Nikon prefer to put the image stabilizing technology in the lens rather than in the body of the camera, but other companies such as Sony place it into the camera body itself.
Currently there is no right or wrong, and it doesn't matter which one you buy. The only disadvantage of having it in the lens is that you often have to pay more money for the IS versions of the lens, for example canons L series lenses can often be $500 more expensive for the IS version.
The best (and cheapest) way to stop motion blur is to simply use a tripod. This keeps the camera still and minimizes any shake.   _{Your Comment}