Electrons like to be electrically neutral. When they are not they quickly look for something to latch on to thereby creating a new molecule. This is how many chemical reactions take place. Without these oxidation-reduction reactions, not only would life not take place, but many of the other important functions of the body wouldn't either. For example, white blood cells often kill their bacterial or viral enemies with free radicals.
Free radicals are like fire.
Properly confined they are beneficial to the body and, fortunately, the body has means to confine them. These are called antioxidants, and they look for excess free radical activity and neutralize it. It is only when free radicals become unconfined and excessive and start attacking normal, healthy tissue that disease takes place. This happens when antioxidant activity is inadequate, hence the importance of maintaining proper antioxidant activity in the body. It is a measure of the overall antioxidant capacity of the body.