In most scenarios in which the skull experiences a large acceleration, it will soon after accelerate in the other direction (if it did not, then it would never stop moving). For example, if the skull impacts a hard surface, but neither the skull and the surface are deformed beyond their elastic limit, then they will behave elastically and the skull will “bounce” back. This type of collision is known as an elastic collision and they will come up again later. As the head moves back, the spine and neck muscles will apply forces that stop its backward motion, possibly inducing a neck injury. Even forgetting about the possible neck injury, this second acceleration presents a new problem. The first skull acceleration + inertia of the brain led to an impact on the front of the brain, then as the brain and skull move backward the second skull acceleration + brain inertia lead to a second impact on the back of the brain, as illustrated in the following image.
Aside from an additional brain tissue injury, the combined swelling of the two opposed injuries will put much more pressure on the brain, increasing the likelihood of permanent injury. This type of injury is known as a Coup Countrecoup , or translated from French by Google Translate, blow, counter blow.