Describe the differences between a Federalist and an Anti-Federalist.
The modern USA has a federal, or central, government; but after the ratification of the Constitution in 1788, there were many who were opposed to placing too much power in the hands of a central government, preferring to keep power with the states. This was because they felt that many of the issues with the United Kingdom lay with the fact that the government had too much power. The terms 'anti-federalism' and 'federalism' need not refer exclusively to the United States, as they can be applied in any nation that has county or regional governments as well as a national governmental body, but for the purposes of this question, I will assume you are referring to the Federalists and Anti-Federalists in the US following the American Revolution.
The Federalists, who wanted a strong and unified national government in order to go about repairing the nation after the damage that had been wrought there by war, were led at their peak by Alexander Hamilton. These people tended to be more educated and more sophisticated, believing that the only way to undo the crippling debt of the young country was to establish a centralized system of banking and a single economic policy for the whole country. Federalism tended to thrive in the larger cities. Federalists supported the Constitution strongly. George Washington was strongly in support of Federalism.
Anti-Federalists, many of whom were farmers and others who lived in the rural areas which had been most damaged by the war, feared that centralized policies would only lead back to the same issues of underrepresentation and economic disparity that had been suffered under the colonial government. They strongly believed in the free agency of states, whom they felt were best placed to act in the interests of the local people. Anti-Federalists included the likes of Thomas Jefferson and James Monroe.