What is wrong if the headlights in a 1995 Ford Explorer will not shut off and you have to disconnect the battery every time you get out of the vehicle what is wrong?

I am not a professional, but an avid Explorer owner (I am on my third). What you are describing sounds like it might be as simple as a headlight relay. Sometimes, the contacts stick together, causing the circuit to remain energized. In other cases, relays coils may fail, causing a "normally open" circuit to become closed. This is usually the case with cars that have alarm or remote entry systems where lights are flashed upon activation, regardless of the headlight switch position. Just a thought.