A glasshouse in the British army is a place where soldiers go if they have done something wrong. It's like a special room where they have to stay for a while. Sometimes it's for just a few days, and other times it can be for a few months.
The glasshouse is called that because it's a place with lots of windows and the soldiers can't hide anything. Everyone can see what they're doing. There are some rules in a glasshouse that the soldiers have to follow, like they can't leave whenever they want and they have to do some work around the place.
The idea of a glasshouse is to give the soldiers a chance to think about what they did wrong and how they can improve. It's like a time-out for grown-ups. When they're finished with their time in the glasshouse, they can go back to their normal duties in the army.