According to Drugs.com zinc sulfate is a mineral supplement that is used primarily for the prevention and treatment of zinc deficiency as well as a number of specific conditions that relate to the normal functions of zinc in the body. The evidence for some of these treatments is highly variable.
The Mayo Clinic features a comprehensive but succinct review of the current state of scientific evidence for the large number of uses for zinc. This list was last updated in November 2013 and states that there is strong evidence for use of zinc in children's diarrhea (where poor nourishment is a factor), stomach ulcers and zinc deficiency. There is also good, though still insufficient, research supporting the use of zinc in acne, ADHD, herpes simplex virus, immune function, sickle cell anemia and Wilson's disease. A large number of other uses were listed but noted to have unclear scientific evidence.