Water damage! Likely mold in lower corner.

Next time, try a more descriptive title so potential helpers will come visit!

Have your roof checked, and are there any water pipes in that wall? That drywall needs to be removed. Its moldy, and if that is an insulated outside wall, most likely the insulation needs to all come out too. Is there a window, above it, where the water could run down inside that corner.

cat-

Looks like plaster walls to me, not drywall. But agree that has to be dug into.

Yep, it does appear to be plaster, but regardless, it needs to be removed. That mold is probably inside the wall.

Ouch, that's major water damage going on. I don't think this is condensation. I'm not an expert, but I'd be looking for a major leak - pipes, flashing, roof.

If this is below grade, stopping the water incursion could be as simple as cleaning gutters and downspouts.

Regardless of the source, I strongly suggest that you open up that wall. I fear you'll find damage worse than mold. You may be looking at some expensive rehab work. :(

This only happens in one half of the house and the other half is just fine.

Is the floor a slab? Is this happening only on the exterior walls? Is any part of the house below grade? How are the walls constructed; what material? Because I suspect that ground moisture may be wicking up the walls. Doesn't look like the typical leaky window type of moisture damage to me.

Unfortunately, I agree with everyone who thinks this is water damage. In fact, if there is so much moisture that it is coming through plaster walls, then there is significant water infiltration and you have to get at the source. My first guess is that it is one or more roof leaks, and once you get that fixed, the problem is that you may well have major structural wood rot inside the walls and mold. It's entirely possible that the plaster will have to be removed from the walls, the rot and mold would need to be removed, and the walls would then need to be re-built. I don't want to sound like an alarmist, but I suspect this has been going on quite a while inside the walls and you need to be prepared for what you might find and what it might cost to fix.

"This only happens in one half of the house and the other half is just fine."

Perfect description of localized roof leaks or gutter failure....

This happened to us and it was a leaking old abandoned swimming pool in the a neighboring yard that had the water turned on inadvertently- the water ran underground down the hill to our house. We were quite puzzled at first. The old abandoned pool had a tall fence around it and when I was walking around the block, I heard running water coming from it and realized what the problem was. Problem stopped when they turned off the water. Now it is filled in thankfully.