To fix the damage, pry any loose material free, patch with compound, sand, and prime/paint with a paint designed for wet areas (preferably mold/mildew-resistant too).
To prevent this from happening again, you'll need to improve ventilation in the area. It's a little hard to tell from these photos, but this looks like a corner within your shower where warm moist air is likely to pool. A drywall or plaster ceiling that is constantly exposed to moisture is going to have these problems again. Consider some of the following options:
- Ensure an exhaust fan is used when the shower is run, and for 30min afterwards to clear moisture from the bathroom.
- Add an exhaust fan, or reposition the existing one, to better ventilate this area (Note: you probably can't safely/code-compliantly put it in the shower area)
- Lower the glass divider, in order to provide an air space along the ceiling so that moisture can disperse more easily.
- Have less steamy showers (your shower head type and position, as well as the typical water temperature, can affect how much steam is generated)
- Make the ceiling more water resistant - better paint and caulking any cracks may be adequate, but you could go as far as adding a waterproofing membrane and tiling it.