Let's take the case of oxidizing agents called free radicals, since they are pretty simple to understand. (In chemistry lingo, the loss of electrons is called oxidation, and since free radicals tend to kidnap single electrons from other molecules, they are technically oxidizing agents: they cause the oxidation of other molecules.)
The notorious free radicals that attack our molecules are reactive because they have, in addition to the usual paired electrons, a single unpaired electron, which is usually an unstable situation for a molecule, depending on where that unpaired electron rests on the molecule. Unstable molecules in general are more harmful than stable ones; they are more likely to attack your body’s own molecules. (To learn more about free radicals in general, see “Free Radicals-what are they?")
Since free radicals have all their electrons paired up except for one, they have an odd number of electrons, unlike the typical molecule, which has all its electrons paired up in twos and thus has an even number of electrons. Stable molecules that have all their electrons paired up are far more common than the rarer free radicals.
Flavonoids in grape, like quercetin, start off with an even number of electrons, but they are able to donate one of their electrons to pair up with the unpaired one on the free radical, so it will no longer be a free radical. This “quenches” the former radical and stabilizes it. However, realize that since quercetin starts off with an even number of electrons and loses one, it ends up with an odd number of electrons. This loss of one of its electrons temporarily turns quercetin into a free radical, too, albeit usually a more stable, less damaging one.
Dose, however, is always important! If you were to take a ton of quercetin, you would have the potential to create many quercetin free radicals in your body! Although quercetin free radicals are somewhat more stable than your average free radical, having lots of free radicals of any kind around is not a healthy environment for your cells!
The quercetin free radical can un-radicalize itself, so to speak, by again donating its unpaired electron, quenching a second free radical. The loss of a second electron gives quercetin an even number of electrons again, making it more stable than before.
Some flavonoids quench, others scavenge. The scavenging flavonoids kidnap the single, unpaired electron from a free radical, becoming a free radical themselves in the process, but hopefully a more stable one. Again, however, stable or not, more is not better. The free radical scavengers and quenchers from plants typically don't reach such high concentrations in our body after we eat them--we could be in trouble if they did! You can't say that for antioxidant supplements--they can too easily be overdosed and turn into the very things we were trying to do away with in the first place. The bottom line is that is seems safest to get your antioxidants from plant foods, rather in isolated supplement form.
There are other, more chemically complicated mechanisms by which antioxidants turn into oxidizing agents. But they basically stem from a similar mechanism to the one above, from switching from one state to another in the process of neutralizing an oxidizing agent.