First off, let's start with how teeth whitening works in general! Just like ingredients in almost all toothpastes, hydrogen peroxide in whitening products remove stains through chemical and mechanical means. Hydrogen peroxide causes the bonds within stains to break, making them break apart and become a lighter color. In some cases, it can remove plaque and tartar, giving you a bright and clean smile. This is the main active ingredient in Mint's whitening gel and whitening foam.
Teeth whitening works best on teeth with a yellowish tint. The tooth's enamel is porous and acts like a sponge, absorbing the stain-causing habits and foods/drinks we constantly expose our smiles to (ie. cigarettes, coffee, red wine, tea). The whitening process restores our teeth to their natural brightness; it does not alter the color of your teeth. That being said, it is natural for teeth to have a bit of a yellowish tint because the dentin underneath the enamel is yellow. How yellow your dentin is varies from person to person. Your age, or how thin the enamel is also plays a factor, as enamel loss causes the yellow dentin to shine through.
Yellow teeth due to enamel loss or aging cannot be significantly lightened. Teeth that have spots due to tetracycline use (grayish tint) or fluorosis will be difficult to whiten as well. Artificial teeth, caps, crowns, veneers, porcelain, composite or other restorative materials does not whiten significantly, but the process does not harm them either.