I take them.  The following isn’t an explanation of “why I take them”, for that, I recommend going to Art’s site.  The following is a primer on what antioxidants are, that’s a good place to start.

An antioxidant is a molecule capable of slowing or preventing the oxidation of other molecules. Oxidation is a chemical reaction that transfers electrons from a substance to an oxidizing agent. Oxidation reactions can produce free radicals, which start chain reactions that damage cells. Antioxidants terminate these chain reactions by removing free radical intermediates, and inhibit other oxidation reactions by being oxidized themselves. As a result, antioxidants are often reducing agents such as thiols, ascorbic acid or polyphenols.^[1]

Although oxidation reactions are crucial for life, they can also be damaging; hence, plants and animals maintain complex systems of multiple types of antioxidants, such as glutathione, vitamin C, and vitamin E as well as enzymes such as catalase, superoxide dismutase and various peroxidases. Low levels of antioxidants, or inhibition of the antioxidant enzymes, causes oxidative stress and may damage or kill cells.

-Excerpt from Wikipedia

Here’s an excellent computer animation clip explaining the process of how an antioxidant works.  It’s basically an ad for acai berries, which  have a very high antioxidant content, but don’t let the sales job for these berries get in the way of the important lesson that the video shows.