The biggest medical breakthrough of the past 125 years without a doubt would have to be the development of the first successful vaccine, the smallpox vaccine, by Edward Jenner in 1796. Jenner's discovery resulted in the further development of more successful vaccines led to the eventual eradication of the disease by the 1970s. Smallpox was one of the most vicious and lethal diseases in history, credited with killing hundreds of millions of victims.
Since then, vaccines are a keystone in modern health and medicine. Countless lives have been protected by the development of multiple vaccines now given to young children and babies to protect their health from disease like polio, turbuculosis, whooping cough, chicken pox, measles.