Alexander Hamilton was one of the most influential of the "founding fathers" because he had so much to do with creating the foundation for the American economy we now have. Hamilton believed in a diversified economy with lots of industry and did things to make that happen. He believed that there needed to be a central bank to help the economy run smoothly and he made that happen. These were very important steps to creating a strong American economy.
Hamilton is controversial because he was abrasive and had strong opinions. He wanted the US to have a monarchy. He didn't mind using government to help the rich if that's what he thought was best.
Opinionated leaders are often controversial, but they can be the ones who are the most influential. This was the case with Hamilton.