Dentists classify tooth stains into two categories; extrinsic - those stains that are on the surface of the tooth, and intrinsic - those stains that are on the inside of the tooth and show through the enamel as discoloration. While whitening toothpastes and chewing gums may be effective for removing extrinsic surface stains, they are not designed to work inside the tooth to remove the darker, more challenging intrinsic stains.
Some form of hydrogen peroxide - either hydrogen peroxide itself or its more stable version, carbamide peroxide - is the most effective material for removing the internal stains. When applied to the tooth, the hydrogen peroxide breaks down into water and radical hydroxyl ions. As these ions work their way through the dentinal tubules and into the tooth, they attach themselves to stain particles and effectively break the stains apart. With the stains removed, the teeth appear whiter and brighter.