The term "Federalist" was used in two different contexts. The first use of the term emerged during the debate over the ratification of the Constitution after the Philadelphia Convention. Supporters of ratification gave themselves the name "Federalists" (and their opponents "Anti-Federalists") to denote their support for the new federal government. Generally, these men were merchants, financiers, and large property owners who believed that the nation needed a more powerful central government. Some examples of leading Federalists are Alexander Hamilton, James Madison, John Jay, George Washington, and Gouverneur Morris. Hamilton, Madison, and Jay penned the Federalist Papers, a series of 85 newspaper articles in New York aimed at explaining the Constitution and persuading New Yorkers to support it.
Shortly after the establishment of the new national government, during the Washington presidency, the nation witnessed the birth of two political parties. This is when "Federalist" took on its second meaning, as the Federalist Party was born. From the 1790s to the end of the War of 1812, Federalists argued for an expansion of the powers of the federal government and policies intended to favor business and emerging manufacturing interests. They were also sympathetic to Great Britain in its war with Revolutionary France. They were still dominated by wealthy easterners, with an increasingly secure power base in New England. Their opponents became known as Democratic-Republicans, and they coalesced around Thomas Jefferson.
So the term "Federalist" is used to describe the original supporters of the Constitution as well as one of the nation's first two political parties.