Where is this wall water damage coming from?
It appears to be a leak - where the leak is could be anywhere from near the damage (but it's usually not) to the roof, and it may not be directly above, depending on the path the water is taking. While I suppose it could be repointing in a brick or stone wall, I'd probably start looking at the roof, unless looking at the outside of the building while it was raining indicated something obvious lower down (a broken or clogged gutter spraying water on the wall, for an example.)