Moisture entrapment is caused by water of course. Somewhere water is penetrating into the wood behind the coating. The source can be from inside the structure, a vent, bad caulk joint, roof flashing, etc. A sufficiently high moisture content inside a structure can also cause entrapment as the moisture migrates through the wall.
Once moisture gets into the wood, regardless of the source, it becomes a problem for any coating. Just as the coating film prevents penetration of the substrate by water from the outside elements, the coating can also prevent any absorbed moisture from escaping from the wood.
The moisture entrapment causes a failure of the coating from blistering, peeling, cracking, and loss of adhesion.
A sure sign of moisture entrapment is sagging paint, (it may even have a pocket of water in it) blistering and peeling. You will usually find a moist surface under the paint film.
The most important thing is to determine the cause of the moisture. No fix will be successful if the source of moisture is not figured out.
Once the cause of the moisture is fixed you will need to examine the wood to determine the extent of deterioration. If the wood is not sufficiently sound it will need to be replaced. If for example the problem is wood siding, scrape away all loose paint and allow to dry. If it is sound and dries out it can be coated. If in doubt replace the wood.
Wood should not have a moisture content greater then 15% to be coated. Use a moisture meter if possible.
I recommend using a quality latex primer like Gripper or Seal Grip. I would use two coats 24 hours apart and top with a quality acrylic latex top coat.