Dental cleaning\scaling is when the dental hygienist or dentist uses specialized instruments (hand and /or ultrasonic) to remove plaque (soft, sticky, bacteria infested film) and tartar\calculus (grey, yellow, brown, black) hard deposits from your teeth without harming them. A few minutes after brushing a thin layer of saliva, proteins, and bacteria (called pellicle) is formed on the teeth which acts as a base for bacterial attachment and growth. Eventually with the accumulation of various species of bacteria and sugars from the foods we eat we get a white\yellowish substance called plaque along our gums and teeth. If the plaque is not removed it will attract minerals from the saliva and harden turning into calculus/tartar. If calculus/tartar is left on the teeth it will provide a situation for bacteria to thrive next to the gums which is detrimental for the health of the gums and can lead to gum disease(gingivitis) which leads to periodontal disease which leads to tooth loss. The purpose of the cleaning is to leave the teeth clean and smooth so bacteria is unable to stick to them, reverse gum disease and prevent the progression to periodontal disease.
Polishing is done after scaling to remove any left over plaque from the teeth and gums and to remove extrinsic stain. It is done using a slow speed hand piece with a soft rubber cup at the end and a special gritty toothpaste-like material.
Fluoride helps to strengthen the teeth from the acids from bacteria in dental tartar and plaque that can weakened them, it also possesses anti-bacterial qualities.