Sodium monofluorophosphate is used in toothpastes to protect tooth enamel from attack by bacteria (cavities, also known as caries). It was developed to avoid infinging on the Crest patent for stannous fluoride.
The active part of the molecule is the fluoride ion, which is why two other fluorine containing compounds, sodium fluoride, and stannous fluoride are also used.
Like stannous fluoride, sodium monofluorophosphate can be used with abrasives that contain calcium, which prevents sodium fluoride from being effective.
Fluorides work in two ways. They reduce the ability of bacteria to make acids, and they remineralize the areas of the tooth that have been attacked by acids from bacteria.