Translation:Its own division is open just for doctors.
The German sentence is grammatically correct but I have no idea in which context it would be used. 'Fachbereich' is either a faculty at a university (university department) or a specialist field of knowledge. Here, it probably means the former, so I guess there is a university department at which only doctors work and study.
No idea. 'There is a special department that's open only for doctors' would probably be a better (although not very elegant) translation. I wouldn't bother digging for answers to deep philosophical questions, here. Sometimes duo just presents weird sentences and enjoys our puzzled faces.
Thanks. BTW found 3 few places in the www where this sentence exists and perhaps the source; this source also has audio quiz cards: http://quizlet.com/40202972/german-education-flash-cards/