This type of ceiling damage is caused by a roof leak. The roofing materials are no longer doing their job and could be worn excessively from age or there could be a small puncture or hole in the roofing.

This ceiling obviously had a large water leak and over time it caused the drywall texture to separate from the drywall. This ceiling also has some sort of mold growing on the drywall. Water damaged drywall should be replaced, if you want the ceiling repair to last a long time.

Once the drywall is wet, it's possible for it to dry out safely with no further damage but you're running a risk over time, because mold could grow on either side of the drywall and actually in a situation like this could start growing between the drywall and the ceiling texture.

When doing ceiling repairs that involve water damage, make sure you replace the drywall or plaster.