Hydrogen peroxide used to be used to clean out bacteria from periodontal pockets. A dentist noticed that over time, patients using this technique had whiter teeth...and so whitening was born.
Most whitening solutions now use a different ingredient, but H2O2 works as well, just slower.
Quote from the book:
'Brush thoroughly with a Sonicare electric toothbrush while sprinkling on the bristles the supplement Active H. Active H is negatively charged hydrogen ions and is probably the most powerful antioxidant in the US. Two hours of brushing produced some seriously white teeth.'