Free radicals have the capacity to causes brain disorders such as Parkinson's Disease or Alzheimer's . They oxidize cholesterol and cause cardiovascular disease . Many other diseases such as diabetes or cataracts are known to be caused by free radicals. They even damage genes which can lead to cancer. Finally, the free radical theory of aging says that it is the primary cause of aging itself.
Free radicals are simply unpaired electrons.
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.