There are several possible causes, some of them normal and others indicating a problem. The pump is controlled by a pressure switch and will continue to run until the pressure in the RVs piping builds to around 45-48 psi. If something prevents that, the pump continues to run.
The pump will continue to run if you hook up to city water and have the tank fill valve open (this does not apply if you do not have such a valve and use a gravity fill system). It will also run if the tank drain or low point drain valve is open. This is normal operation. Close those valves and the pump should stop within 5-15 seconds.
If all the valves are set properly and you are hooked to the city water supply, the pump may continue to run if the city water inlet check valve is bad - essentially you are pumping water back into the campground if that happens.
A leak in the RV plumbing system will prevent it from pressuring and the pump will continue to run or will cycle on/off regularly. Look for the leak if this happens.
A bad check valve in the pump inlet from the tank will allow water to seep back into the tank, causing the pump to cycle on/off repeatedly when no water tap is open. This does not usually cause the pump to run continuously, though.
If the inlet to the pump cannot draw sufficient water, due to a leak (sucking air) or a clogged pump inlet (or inlet filter, if so equipped), it will continue to run.
Last, it could be a defective pressure switch, but this is pretty rare. It the last thing I would suspect when faced this sort of problem.
Disconnect from city water, make sure there is sufficient water in the tank, set the valves for normal operation and turn the pump on. If it pressurizes within 5-20 seconds and stops, the pump, switch, and inlet are probably OK and there probably are no major leaks in the RV piping (unless the pump cycles back on repeatedly after initially shutting off). If it works OK that way, then hooking up the city water was the problem and was either a valve open or a bad city water inlet check valve.