"Morbus" is Latin for "disease," so "Morbus Brightii" was Bright's disease, a kidney ailment:

http://www.whonamedit.com/doctor.cfm/1984.html
... "Within few years after the description of "his" disease, Bright's name was known everywhere. The complex of symptoms of edema with albuminuria and affections of the kidneys soon was known as Morbus Brightii, even though other names had been suggested. A large number of articles and books tell of the intensity of the research." ...