What is a federalist?

In the context of American history, a Federalist was someone who believed in a stronger Federal government and that political power should become more centralized. To this end, Federalists tended to be staunch supporters of the Constitution.
After the Revolutionary War the United States needed to take its place among the community of nations. However, under the loose governmental structure of the Articles of Confederation, it was unable to do so. Ultimate authority resided with each state, so it was impossible for the United States to pay off debts incurred during the war, to settle territorial disputes with foreign countries, or even to maintain good order against the threat of domestic sedition. The United States needed to speak with one voice in so many important areas of policy, but couldn't.
It was these conditions that gave rise to changes in American government as set out in the Constitution. These changes were generally welcomed by the Federalists. Opposing them were the Anti-Federalists. They thought that the Federalists wanted to invest central government with too much power. To them, this smacked of tyranny; and as Americans had just fought a war against what they perceived as British tyranny, the last thing the Anti-Federalists wanted to see was its return to American soil under a different guise.
Anti-Federalists strongly believed in "The Spirit of '76," the ideal of republican liberty set out by Thomas Jefferson in the Declaration of Independence. According to this principle, ultimate political authority must reside with the individual states, and not with a remote, potentially despotic federal government. It was to assuage the concerns of the Anti-Federalists that the framers of the Constitution added the Bill of Rights as amendments to the original charter, ensuring that the final document was a compromise incorporating both Federalist and Anti-Federalist elements.
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