That fitting is the "city water" supply connection. In a campground that has water at the campsite, you screw in a potable water hose to that connection and it supplies the camper with pressurized water. That fitting does not fill the onboard fresh water tank that the water pump draws from.
The problem is, the gray nut is loose, the rubber cone washer in the fitting is dried up, cracked and leaking or both.
You need a new cone washer installed and the fitting tightened and it should stop the leak. You can try and tighten the nut and see if it stops, but long term be getting a new cone washer.
The gray nut will unscrew from the brass fitting. Look inside the gray nut and the cone washer should be there. Sometimes it sticks to the PEX fitting (the gray nut part) and sometimes it sticks to the brass city water fittings.
If the washer is stuck in the fitting, using an ice pick of sorts you can stab it and pluck it out. Be careful to not push the gray fitting into the wall as I do not know your floor plan if you can get to the back side to poke the water piping backout.
What you are looking for is a 1/2" PEX swivel cone washer. Odds are high you will not find just the washer for sale at your local lumber yard or hardware store that sells PEX fittings.
I am working on a post (in the future) on how to find a replacement cone washer but here is some help before then.
Go to your lumber yard or plumbing place and ask for a 1/2" PEX to 1/2" FNPT straight swivel fitting. A straight fitting is usually cheaper than a 90 deg elbow fitting and plastic PEX in place of brass is even cheaper yet. You are then going to buy the entire fitting and take the cone washer out of it and use that in your camper city water connection. The whole fitting can run between $4 to $6 bucks.
Here are some pics.
A collection of several brands of PEX swivel fittings.
A close up,
Here is what the come washer and fitting looks like in the wall. This is a 90 deg elbow, but the cone washer and the nut is the same as what yours is.
The fitting less the nut
The fitting with the nut, this brand is white where yours is gray.
I have tracked down just the replacement washers, but it will take some time to get them from on line. The local lumber yard buying the whole fitting will be faster, just more expensive.
This is the actual Flair-it brand replacement cone washer. It is the only brand I can find out of 6 others PEX manufacturers that sells just the cone washers as a replacement part.
You can buy a pack of 10 of those Flair it washers for $0.98 cents from Amazon as an add on item, if they have them in stock. They go out of stock often. Being an add on item Amazon wants to to buy $25 of stuff sold by them and they will ship the 10 pack of washers with it. No one wants to deal with the freight of shipping 1/2 ounce of rubber cones for $0.98 cents.
See here https://www.amazon.com/gp/product/B0...?ie=UTF8&psc=1
Hope this helps
PS, when you screw the city water flange back onto the side of the camper, you should replace the sealing tape between the siding the the white flange. I use butyl sealing tape. 1/8" thick by 1" wide. It comes in a roll.