The answer is: Activated charcoal LOVES tannins.
And tannins (found in MANY foods, coffee, tea, wine, etc., and ad nauseum) are typically what cause staining and dinginess of the enamel of your teeth. It loves the tannins, and the tannins love it more than they love your teeth, so off they’ll go. Hopefully.
However, and here’s the good part, activated charcoal doesn’t adsorb the calcium salts tooth enamel is made of. It’s almost like it was made to whiten. And brighten. And do no harm.