Before one can truly understand what a free radical is and how it works, a bit of a chemistry lesson must take place. Don't worry, this won't hurt a bit.
A variety of different living cells make up the human body. These cells are made up of molecules and these molecules are made up of atoms. Atoms are made up of a nucleus, neutrons, protons, and electrons. The number of protons, which are positively charged, dictate the number of electrons, which are negatively charged. The electrons - yes, even with their negative attitude - are particularly important: they orbit around the atom, cause chemical reactions, and bond atoms together to forms molecules (which ultimately form cells).
Electrons travel around the atom in shells. The inner shell is considered full when it has two electrons; after two, the electrons begin to fill the other shells. The outer shell - and how many electrons are in it - is the biggest factor in determining the atom's chemical behavior.
Atoms, like most of us, aim to find some sort of stability. For this reason, they try to fill their outer shell by gaining or losing electrons, or bonding with other atoms and sharing electrons. Once this bonding takes place, a molecule is formed.
Normally, after bonding, all electrons in a molecule are paired: there is rarely a lone electron by itself. But when this does happen, free radicals form. Desperate and unstable, free radicals do whatever it takes to capture the electron they need to stabilize themselves. This desperation and instability causes free radicals to attack nearby molecules. If the molecule under attack loses an electron, it becomes a free radical and repeats the process. A domino effect then begins and the living cell is harmed.
Every person has free radicals in their system; there is really no way around them. Some are part of our metabolism and some are used as defense mechanisms by our immune system. But, factors that lie outside the body - such as pesticides, tobacco smoke, gasoline fumes, and air pollution - can create free radicals as well. This is where anti-oxidants become particularly important.
Luckily, anti-oxidants are leading the free radical counter movement. They lead it by donating their electrons and stopping free radicals from needing to attack. When the anti-oxidant donates an electron, they don't become free radicals simply because they have the ability to remain stable in a variety of states.
Essentially, anti-oxidants are the police force of the human body: they travel around looking for free radicals and attempting to neutralize them before they can do any damage to living cells. This makes consumption of anti-oxidant properties - such as fruit, vegetables, wine, and anti-oxidant infused water - particularly important: the more policeman you have on staff, the better chance the bad guys will be caught before they begin a damaging crime spree.