A deep cavity may reach the point of also involving the pulp of the tooth, which inflames it and makes it go into necrosis. In this case the nerve fibres in the pulp alert you of that annoying localised hypersensitivity.
The dental pulp is removed with devitalization, also called root canal treatment, to prevent the inflammation from giving rise to an abscess or a granuloma. The operation is performed with local anaesthesia.