The tooth is composed of an outer enamel layer and an inner dentine layer.The dentine has microscopic tubes running through it which are filled with fluid. When the dentine shows either as a result of gum recession or wear of the enamel, the tubes are exposed. When a stimulus occurs such as hot or cold drinks the fluid in the tubes moves and in turn this stimulates the nerve to send pain signals to the brain.
The active ingredients in toothpaste help to obturate the endings of these tubules which consequently stops the stimulus effecting the fluid and the nerve. Often I recommend a sensitive toothpaste as a topical treatment after brushing and to use the toothpaste last thing at night smeared on the teeth and left on overnight. This speeds up the process and allows the therapeutic agent to be in contact with the dentine for a longer duration than when used in brushing alone.
I hope this helps,
Sunita