There are several reactions that occur. Not only is there the stopping against the ground that causes many injuries in different parts of the body, there is the involuntary muscle reaction that occurs as soon as your brain discovers you are on the way down.
The obvious injuries to the knees, elbows, hips and arms usually get most of the immediate attention and often heal up within a few days or weeks depending on how far you fell, your age and the surface on which you landed.
The spine is most often affected with by a fall. Each joint reacts to the force of stopping and usually becomes jammed together. Some joints come together so far that they can no longer endure some of the normal movements. Sometimes slipping and falling can cause damage to the spine without causing immediate symptoms. After hours, days or even weeks, the joint capsules may become inflamed and back pain is the result. Because of the time lag since the fall, people often forget and don't make the connection.
It is wise to have a spinal check up after any kind of a fall to make sure there is no hidden or underlying damage.