When you combine them, the meaning is incredibly logical and transparent: 病 (sickness) + 房 (room) = a room for the sick, or a hospital ward.
In a Western context, a “hospital room” is a straightforward, functional term. In China, the concept of a 病房 (bìngfáng) carries additional cultural weight, primarily related to social obligations and family involvement.
You will encounter 病房 (bìngfáng) in any context related to being hospitalized.
The term itself is neutral and formal enough for any situation.