There are (generally) two ways to get water to your fixtures in your camper.
1. City water (pressurized line that your picture shows currently connected).
2. On board potable water tank. You fill this tank through the opening you are asking about using a pressurized water supply when you are planning to travel to a site that does not have water hookup available. It also provides water while you are on the road. There is at least one switch inside the camper marked "pump" or similar. This has to be turned on in order to pressurize the system and pump water to your fixtures.
If you look at the underside of your camper directly below the water fill port you should see a short tube with valve hanging down. This is the drain line for the fresh water tank. Since you are on city water you don't really want a tank full of water sitting stagnant and growing algae. Reach under and open the valve to let the tank drain down. It'll take a while.
As mentioned before, you probably have a check valve in the pump that is leaking by. If this is not addressed the system will continue to allow water into the tank. Sometimes it's easier to add a check valve to the line than to mess with the water pump itself.