Tartar is the result of plaque that hardens over a period because of mineral deposition in these build ups. Normal brushing at home is not always enough to remove these hard deposits as they are normally in hard to reach places and impossible to remove with the soft bristles of your tooth brush.
Professional cleaning is needed to remove these deposits and is normally conducted by your oral hygienist or dentist who makes use of different techniques which mainly includes the use of either hand instruments or an ultrasonic scaler (or a combination of both).
Firstly, the bulk of the deposits are scraped of and then the rest of the tooth surface is cleaned by a scaler (hand or ultrasonic). The second step is to polish these tooth surfaces by making use of a soft brush (or cup) and a polishing paste. This ensures that the surfaces are smooth and stain free leaving them bright and shiny. By removing the stains and plaque (tartar) there are no rough patches for plaque to adhere to preventing build up and making it easier to clean at home.
There are a lot of advantages to doing a scale and polish but the major advantage of having a polished teeth surface is that the food particles do not stick to smooth surfaces easily reducing the chance of food and plaque depositing on the teeth.