Dentin hypersensitivity (DH, DHS) is dental pain which is sharp in character and of short duration, arising from exposed dentin surfaces in response to stimuli, typically thermal, evaporative, tactile, osmotic, chemical or electrical; and which cannot be ascribed to any other dental disease. Source: Wikipedia
The most common form is dental sensitivity to cold temperatures - which, depending on the study, has been reported in 4% to 74% of people (note margin of error). It can affect any age-group.
The cause of dentine sensitivity has been extensively investigated - and there are currently several competing theories. Including the 'direct innervation theory' the ‘odontoblast receptor theory’, and the ‘hydrodynamic theory’ - that latter of which is the most commonly accepted. For details see :Journal of Conserv Dent. 13(4): 218–224
Several brands of toothpaste attempt to desensitize the exposed dentine. They typically use potassium nitrate, potassium chloride or potassium citrate. They can be an effective 'home treatment' - but the 'mechanism of action' has not been definitively confirmed
Potassium-containing toothpastes are common; however, the mechanism by which they may reduce hypersensitivity is unclear. Animal research has demonstrated that potassium ions placed in deep dentin cavities cause nerve depolarization and prevent re-polarization. […] It is believed that potassium ions diffuse along the dentinal tubules to inactivate intradental nerves. However, as of 2000, this has not been confirmed in intact human teeth and the desensitizing mechanism of potassium-containing toothpastes remains uncertain. Source :Wikipedia