An antioxidant is any molecule that is stable with or without all its necessary electrons. A free radical, on the other hand, is a molecule that is unstable when it loses an electron.
An unstable free radical causes damage to nearby healthy cells when it "bounces" around looking for an electron to steal. A damaged healthy cell is the cause of aging, illness and disease.
The purpose of an antioxidant is to donate one of its electrons to the unstable free radicals. Once it has done that, both molecules are stable.
Antioxidants, therefore, are nature's solution to that problem.