Generally speaking, you’ll find that there are two teeth whitening solutions that are often used:
1) Hydrogen peroxide
2) Carbamide peroxide
Both whitening solutions are effective, but you’ll often find that hydrogen peroxide is used if you want a quick whitening solution, while carbamide peroxide is used if you have long periods of time for whitening (eg. overnight).
In both scenarios, these solutions work to break apart chemical bonds that occur on both organic and inorganic tooth stains.
In addition, the solution works on both extrinsic (eg. stains on the outside of the tooth likely caused by lifestyle choices like smoking, coffee/wine consumption) and intrinsic stains (eg. stains that are part of the tooth and are more likely due to aging/genetics).
Extrinsic tooth discoloration tends to be easier to treat, while intrinsic is tougher and may require a dentist’s expertise. Having said that, if your teeth are looking less white than you would like, you can benefit from teeth whitening — regardless of what type of staining you have.