Antioxidants are very good for prevention of diseases like heart disease and cancers. Antioxidants like vitamin E may protect against cardiovascular disease by defending against plaque formation in the arteries.
Antioxidants like vitamin C defend against cancers of the mouth, larynx and esophagus. To consume antioxidants became popular in recent years thanks to studies made in the past decade.

It is not possible to give a simple definition but it can be explained as below.
As free radicals (see below) have deficiency of electrons, compounds are needed which can neutralize free radicals by donating their own electrons to free radicals but they themselves do not become free radicals in the process. This stops the electron-"stealing" chain reaction.
The antioxidants themselves do not become free radicals by donating an electron because they are stable in either form. Antioxidants convert free radicals to harmless waste products that are eliminated from the body before any damage is done to the body.
Thus the antioxidants act as scavengers, helping to prevent cell and tissue damage.

Flavonoids belong to a group of natural substances with variable phenolic structures and are found in fruit, vegetables, grains, bark, roots, stems, flowers, tea, and wine (1). These natural products were known for their beneficial effects on health long before flavonoids were isolated as the effective compounds. More than 4000 varieties of flavonoids have been identified, many of which are responsible for the attractive colors of flowers, fruit, and leaves (2). Research on flavonoids received an added impulse with the discovery of the French paradox, ie, the low cardiovascular mortality rate observed in Mediterranean populations in association with red wine consumption and a high saturated fat intake. The flavonoids in red wine are responsible, at least in part, for this effect (3). Furthermore, epidemiologic studies suggest a protective role of dietary flavonoids against coronary heart disease (2). The association between flavonoid intake and the longterm effects on mortality was studied subsequently (4) and it was suggested that flavonoid intake is inversely correlated with mortality due to coronary heart disease (5).

Flavonoids: a review of probable mechanisms of action and potential applications 1–3 (part)
The american Journal of Clinical Nutrition, 2001
Robert J Nijveldt, Els van Nood, Danny EC van Hoorn, Petra G Boelens, Klaske van Norren, and Paul AM van Leeuwen