To medicate is to treat an illness with some kind of medicine. You might not need to medicate your bad cold, but you'll most likely need to medicate your strep throat.
A doctor will medicate diseases that are diagnosed and can be treated with medicine. If your doctor, for example, decides to medicate you with antibiotics, it means she believes you have an infection caused by bacteria. Medicate comes from medication, from the Late Latin word medicari, "to medicate, heal, or cure."