Dental cleanings involve removing plaque (a soft, sticky layer of bacteria, food & saliva) and hard tartar (calculus) deposits that have built up on the teeth over time. Your teeth are continually bathed in saliva which contains calcium and other substances which help strengthen and protect your teeth. While this is definitely beneficial, it unfortunately means that we tend to get a build-up of calcium deposits on the teeth.
If this tartar is allowed to build up on the teeth, it will unfortunately provide the right conditions for bacteria to thrive beside the gums. The purpose of cleaning and polishing is basically to leave the surfaces of the teeth beautifully clean and smooth so that bacteria are unable to stick to them and so provide you a better chance of keeping the teeth clean during your regular daily hygiene regime.