Primarily, the Eiffel Tower was built for the World Exhibition. It was called Paris Exposition in 1889. The exhibition was organized to celebrate the 100th anniversary of the French Revolution. The purpose of building Eiffel Tower in such structure was to show to the world France’s advancement of technology and beauty. The Eiffel Tower was designed by Gustave Eiffel. It seemed that then the name of the tower was derived from the designer’s last name, “Eiffel”
Another reason on why the tower was built was for scientific progress. Although few realized it, the Eiffel Tower would become the prominent structure in terms of science and technology. Many experiment with temperature, pressure and pendulums were performed atop the unique famous building. Additionally the Eiffel Tower was used for radio transmission tower. Many experiments were conducted atop the Eiffel Tower for radio transmission advancement. Once the Eiffel Tower was proposed to be demolished but it was spared because the tower had the promising future as a radio tower.
(Simplified from http://ezinearticles.com/)