Photos taken with a camera do not represent a single moment of time. Due to technological constraints these shots stand for some scene over a brief period of time. This time frame depends on the camera’s shutter speed. In motion blur, any object moving with respect to the camera will look blurred or smeared along the direction of relative motion.
Motion blur is frequently used to show a sense of speed. You can achieve this effect in a usual scene using slow shutter speeds. You may want to take a look at resources provided in the end of the article — they show how one can add the motion blur effect in photos.