Federalism often refers to the beliefs of the Federalist party. This political party believed that the United States needed a strong federal (aka central) government in order for society to run well. This was based of several different factors including the lack of success of the Articles of Confederation (which had created a weak central government) and Shay's Rebellion.
On the other hand, people against the idea of federalism were worried that the federal government would gain too much power. Instead, they preferred for state governments to have a majority of the power. They used the American Revolution as their reasoning as to why a strong central government would not work well in America.