I want to create a world where magic is based on the elements. How would the respective elements have an impact on society?
Yes. The ability manipulate water would impact both medicine and trade. A large percentage of your body is made of water a doctor with the ability to manipulate water would be extremely effective. And a mage that could manipulate the sea could vastly increase the speed of trade ships. This could have a vast impact on culture and the overall spread of ideas.
The ability to manipulate air. Could I have an impact on farming. Droughts had devastating consequences to the ancient world. If you have farmers that could manipulate the wind to blow rain clouds to your nation or country you could vastly increase your amount of food production which would then increase your population and overall health and wealth of your nation. If your air mages were powerful enough to fly then they can serve as a postal system quickly sending messages from one location to another.
The ability to manipulate fire and/or heat would be extremely useful to a chemist or scientist. Many chemical reactions require a large amount of heat.
The ability to Earthbend would completely revolutionize the construction of cities and monuments. If your mages could also manipulate metal then could be even more useful to construction. Skyscrapers and Great Pyramid size monuments could become commonplace.