The vast majority of toothpaste action is simply mechanical. Over half of the ingredients in any any given toothpaste are simply abrasives, designed to scrape the disgusting gunk away from your mouth. Aluminum hydroxide, calcium carbonate (yes, the same calcium carbonate that forms shells for marine life, snails and eggs), dicalcium phosphate, and silicon dioxide (otherwise found in sand, quartz, and diatom frustules), among others. As you brush your teeth, you simply scrape away the goop from your mouth.
|This picture was totally not posed at all.|
One of the most notable benefits of toothpaste is the addition of fluoride (usually in the form of sodium fluoride). Fluoride is an anion, a negatively charged molecule. When the halogen fluorine picks up an extra electron, it becomes F-, the anion that matters for your teeth. Sodium fluoride, the most common way of getting fluoride in your toothpaste, is an ionic compound, meaning that it dissolves into sodium ions (Na+) and fluorine ions (F-). Of course, many other additives exist to direct fluoride to your teeth; hexafluorosilicic acid and salt sodium hexafluorosilicate, for example, are the versions usually used in drinking water.
When fluoride is included in toothpaste, low concentrations of fluorine ions hang out in your saliva. This reacts with the calcium phosphate in your teeth, forming a mineral called fluorapatite. This process, called remineralization, can help fix a just-beginning-to-form cavity. It also interferes with the biological functioning of cariogenic (cavity-causing) bacteria such as Streptococcus mutans.
Triclosan, an antibacterial agent, is also a common toothpaste ingredient, serving to prevent both plaque and gingivitis. Some toothpastes will also contain detergents (such as sodium lauryl sulfate), flavorants, and additional remineralizers.