When hydrogen peroxide acts as an oxidizer it itself is reduced. Broadly this means that the peroxide bond is broken and that water is formed.
However, why is there a tendency for hydrogen peroxide to be such a potent oxidizer in acidic media?
In acidic solutions, H2O2 is one of the most powerful oxidizers known—stronger than chlorine, chlorine dioxide, and potassium permanganate.
Why is it not as potent without added acid, i.e. 3% hydrogen peroxide, the stuff you find in medicine cabinets, isn't a very good oxidizer?
The "duh" answer is that hydrogen peroxide is especially unstable in acidic media. But why can't acidic media stabilize hydrogen peroxide, and specifically the peroxide bond?
Simple electrostatics tells me that having a bunch of positively charged hydronium ions around the positively polarized oxygens in the peroxide bond isn't a "good" situation. Of course there are anions from the dissociation of the strong acid but these anions necessarily have diffuse negative charge, which is probably not enough to stabilize the polarized peroxide bond to significant extent. Is there anything else?