Alexander Hamilton is important mostly for what he did while George Washington was president. He was also a major American figure in the Revolutionary War, but it was his work in government that is most important.
Hamilton was the first Secretary of the Treasury under the government created by the Constitution. In this position, he created the financial structure for the United States. He set up a system for funding the national debt. He proposed a national bank and a tariff. He did these things because he wanted to set up a stable economic environment that would allow the United States to eventually become a wealth and industrialized nation.