Are formed in the body by exposure to natural ionization from the earths supply of radioactive elements and high energy cosmic rays from space, and a few other ways. They are highly reactive chemical intermediates which react so fast that they can "chew up" any other molecule in the intermediates immediate environment, including DNA and proteins and many molecules that we produce in the building of our bodies. Evolution has developed to give some protection when genes are damaged, but it can't always repair the damage, so, some cells react to being damaged by apoptosis (cellular suicide) as a way to mitigate the copying of damaged information, which if left unchecked leads to cancer and other diseases.
That is why we breed when we are young and haven't accumulated a whole lot of damage to our cellular reproductive and maintainance systems. Time allows the accumulation of such damage by free radicals and accelerates as we are getting older. This is a "problem" for ALL life forms.
Antioxidants, are molecules which a free radical reacts with faster (hopefully) than our own neccessary biochemical systems, and so "gobble up" free radicals, before they have time to do serious damage to a cell. This of course relys on what type of antioxidants one takes as a supplement. Nature has provided us with many natural antioxidants, but since they must be in the cell in a relatively high concentration (remember, a free radical reacts very quickly with whoever is in its "neighborhood". If you take lots of both fat and water soluble antioxidants, then you gain "some" protection against cell catabolism in the average cell life cycle.