It means a large number of people either falling ill or dying.
It is generally used in the context, where people drastically get affected with some sort of diseases and fall ill in numbers.
Generally used in communities where the disease is epidemic and when one sees people falling ill like swarming bees around sugar.
1)When the plague hit Maharashtra, people were dropping like flies.
2)It was in the year 1997, when many people started dropping like flies by drinking water and were affected with Cholera.
3) Any drastic epidemic disease will make human beings drop like flies.
4) People of Africa have the habit of dropping like flies as they have no proper health care centers.