Anti-oxidants "quench" free radical molecules and by doing so help prevent illness and the aging process. Free radicals are very active chemical groups and have been shown to cause or worsen all diseases. There are many different types of free radicals and they occur in every organ in the body.
Fortunately, the body also produces several different types of anti-oxidants (e.g. - glutathione). Anti-oxidants are also absorbed from the foods that we eat. The types of anti-oxidant molecules absorbed from our diet are very important because not every anti-oxidant is capable of reacting with every free radical to stop the formation of new free radicals. In other words, some types of anti-oxidants are specific to certain types of free radicals. Additionally, the location where the body stores these absorbed anti-oxidants is key. (For example, if the absorbed anti-oxidant is stored in the liver this anti-oxidant will be not be available for stopping free radical spread occurring in the lung.)
In general the best way to get your anti-oxidants is by eating a sufficient quantity of a large variety of fruits and vegetables. Unfortunately many of us do not, so the next best way is to take anti-oxidant supplements to assist in quenching free radicals.