Enamel, the top layer of the components that make up teeth, is the hardest, mineralised substance in the body (predominantly made from hydroxyapatite). The enamel layer of teeth does not contain living cells, in contrast to the other hard (cementum and dentine) and soft (pulp) dental components. Hence cracks or chips of the enamel layer do not heal and damage to the enamel layer is permanent.
Despite being protected by the hard enamel layer, teeth can crack, chip and break. Such damage can be caused by biting on something hard, by accidents such as falling on the face, by other impact such as being hit in the face, by cavities from dental decay or from general neglect of extensive old fillings.
A broken or chipped tooth may or may not be painful but a sharp broken surface is likely to irritate or hurt the tongue and/or other soft tissue in the mouth. A broken tooth is more likely to be painful if the pulp (containing the nerve of the tooth) is damaged or the (innervated) dentine layer of the tooth is exposed.
Further reading: Diagnosis