How does a water pump in a water cooler work?what are its parts .the picture of the water cooler is given in attachments.how to repair it?
I think the most common arrangement would be a small centrifugal pump driven by an electric motor.
If it isn't working, there are a number of possibilities...
(1) the water in or out is blocked
(2) the electric motor has failed
It is really a matter of checking the simplest/easy things first (eg is water in? does the motor run?) and then deciding whether to repair or replace.
Is electrical power getting to the pump? Check volts at the switch and on any connector block (carefully). Does it hum when it's supposed to be on?
It looks fairly elderly to me. Perhaps it has some corrosion inside it. Have you tried eBay for a replacement? If you can find a cheap one and it the present one passes all the tests that have been suggestion then it may not be too upsetting to fork out for a replacement.