A scale and polish cleans your teeth very thoroughly.
Scaling removes the hard tartar which forms on your teeth like scale inside a kettle. You can't remove it just by brushing your teeth. Scaling also removes trapped food and plaque containing millions of germs, which can cause tooth decay and gum disease. Stains from coffee, tea, cigarettes or red wine are also cleaned away when your dentist polishes your teeth.
A dental hygienist is specially trained and will scale your teeth. If you clean your teeth very thoroughly anyway, your scale and polish will take less time.