Hydrogen peroxide is a bleach - it delivers Oxygen pretty much directly to the place it is needed. H2O2 breaks down to H2O and O - which does its job. It is kinder than chlorine bleaches but only because it is so dilute when you get it. The Germans used close on neat H2O2 to fire some of their rockets in WW2§ and has been a constituent chemical in the bombs let off in London over the last couple of years.
But it does do a fine job on nappies
BB