Dual federalism is a political system in which power is divided very clearly between the states and the federal government. More importantly, each level of government is able to work without any interference from the other level.
This was close to the system that the United States had between 1837 and 1937, when the power of the states was very significant. However, this period is considered to have ended during Franklin Roosevelt's presidency. This was a consequence of the fact that the New Deal policies were decided to be constitutional by the Supreme Court, forcing the states and the federal government to work closely together in a way that they had not done in the past.