It could be many things. Roof above? Pipes in the ceiling? Condensation from something exposed to out door temperatures? It depends on what above the area of the leak. Once you determine what that is then you most likely will have pin pointed your culprit.
I spent the better part of yesterday hanging some sheet rock at my brothers home...the ceiling in his home office is below the mater bath. A pin hole leak developed in some plumbing....needless to say it created a problem.
In the course of the repair I noticed damage further out from the "hole"
As Paul said, lots of things can cause damp spots. Sometimes they are not quite as easy to determine the cause as one would think.
I would first think that its a bathroom issue and would want to rule that out. Check behind the toilet first. Using a dry paper towel as a blotter. Simply touch the exposed water pipe around the valve, the pipe that connects to the toilet, the space around the tank and toilet first. Keep checking the towel for water. Then using your knee, lightly push to the side the toilet to see if it moves. Does it rock? Then that is a sign that perhaps the wax ring is leaking. The wax ring is what seals the toilet to the plumbing.
Then check around the shower/tub area. Is the floor in good shape there? Next time someone uses the shower tub area place two paper towels on the floor next to the outside edges of where the shower tub meets the floor. Is the towel wet once the bath is complete? Could be water overflow.
Does water drip out from behind the tub/shower faucets when you use them? Packing in the valve could be allowing water to leak behind the wall when using them. Very common issue.
If you have a tub, the handle within the tub to stopper the water can be an issue as well. If the gasket is leaking around this device water that splashes against it can cause leaks down behind the tub on occasion.
Also drain connections to shower floors can be an issue. Plastic shower pans leak a lot when the rubber seal that connects the pan to the drain pipe comes loose.
These are just a few of the items that your stains can be coming from. Figure out the location to reference to what ever is located above and you will be fairly close to the leak most times.
Keep us posted on what you find.