Before we get into the details of tooth-whitening, let's take a minute to meet the enemy. What are tooth stains anyway?
Each of your teeth is made up of an inner dentin layer and a hard outer enamel layer, which protects the teeth. When you put stuff in your mouth -- food, cigarette smoke, coffee, etc. -- another layer gradually forms on top of the enamel layer. Basically, the foreign material accumulates to form a pellicle film over the enamel layer.
A dentist can clean away this film, through scraping and chemical treatments. Even brushing your teeth can knock out some of it -- brushing with the abrasive toothpaste cleans the tooth in the same sort of way scrubbing with an abrasive pad cleans a dish. "Whitening toothpastes" are designed to work even harder on this layer.
The problem is, as this pellicle layer sits on your teeth for years and years, the foreign material gets into the enamel. The enamel layer is made up of hydroxyapatite crystals, which form microscopic hexagonal "rods." Simply put, enamel is porous, which means staining agents can work their way down into the tooth, where you can't simply scour them away. The deeper stains are basically harmless, but many people find them unattractive.
This is where true tooth whiteners come in. Basically, the whiteners use bleaching chemicals to get down into the tooth enamel and set off a chemical reaction (specifically, an oxidation reaction) that breaks apart the staining compounds.
Most tooth whiteners use one of two chemical agents: carbamide peroxide or hydrogen peroxide (the same stuff that will bleach your hair). When used in the mouth, carbamide peroxide breaks down into hydrogen peroxide and urea, with hydrogen peroxide being the active whitening ingredient.
There are a number of different ways of setting off this basic process. Let's look at the main options.