To be innovative is to think up new and creative ideas. These ideas would be advanced and original. Some innovators go against mordern ideas or customs because they strongly believe more in their idea. Innovators are usually the people that come up with new inventions and theories. These people are the ones who "think outside the box" or the ones that break the rules and do things their way.
An example of an innovator is Nicolaus Copernicus. He expanded on the heliocentric theory, the theory that everything revolves around the sun. He promoted and believed in that theory though it was widely belived that everything revolves aroung the Earth. Even though he was shunned for believing in the theory and it was against his own religion, he still believed in it.