Translation:The room of the library
It's because 의 shows possession. Like in 제인의 개 which means 'Jane's dog' or 'dog of Jane'
whar does difference between 'the room of library' and 'the room of the library'
The audio on this isn't the best in my opinion. "방" sounded like "간" or "갈" to me. But maybe I just need more listening practice