I presume you have a submersible pump. I agree with JCLoughie's suggestion, but for future reference one of the most common causes for a pump failure is allowing the pump to run whilst the water container is empty, or for any reason the pump does not shut off when the taps are closed.
The reason this is damaging, is the pump consumes up to 100W peak power some of which it converts into heat. It relies on the flow of water through the pump to keep it cool. If the flow of water is blocked the temperature of the pump will begin to rise, It will rise even more quickly if the water carrier is empty. The temperature can rise far enough to soften the plastic of the pumps motor housing which can distort and damage the motors water seals. When water is available it can get into the motor and when that happens the motor will fail quite quickly.
You need to know if your pump is controlled by microswitches in every tap (a micro switched system) or by a single pressure switch (a pressure switched system)
If its a micro switched system, then whenever a tap is just cracked open a micro switch in the taps body closes and completes the power circuit for the pump. If a micro switch fails to break the circuit when the tap is closed, the pump will run continuously. You need to check every tap including the shower water valves are turned off completely. I have had to point this out on a number of occasions to folks whose shower had a mixer tap and a trigger on the shower head.
If its a pressure switched system, the pump runs to increase the pressure in the pipe work and when it rises far enough the pressure switch interrupts the pump circuit and turns it off. When you open a tap, the pipe pressure is released and the pump turns on. if your tap is only open a little, the pump may repeatedly switch on and off as it may be able to create more pressure than the cracked open tap releases. That is normal behaviour. Normally in a pressure switched system the pump will stop running in under 5 seconds from fully closing the tap.
If the pump takes more than a few seconds to turn off after the tap is closed, it suggests the pressure switch may need to be adjusted - the instructions to do this should be in your caravan handbook or they can be found on the Whale pumps (Munster Simms) website. This is voltage dependant which can change if you switch from using an mains Electrical Hook Up (EHU) to just caravan battery.
However if the pump continuously pulses even when the taps are closed, it means you have a water leak somewhere. In some cases there is no visible leak, in which case its probably debris in the non return valve which is usually fitted into the pressure switch. Sometimes these can be repaired by dismantling the pressure switch and cleaning the parts before reassembling it. Other wise it may need a replacement pressure switch .