Federalism was Madison's attempt to find a compromise between the Hamiltonains and Jeffersonians. They were the Founding Fathers of the US Constitution.
The term Federalism means a vertical separation of powers. Political power is divided between a national government and state government each having their own area of Substantive Jurisdiction. This means that the national government and state government are two sovereign bodies. Federalism means that the two level of goverment are not to interfere with each others specific powers. Federal governmet have the power to declare war, maintain army service, control over immigration and so on whilst state government have the power over education, health care, drugs, death penalty, age to get marry or buy alcohol and regulating elections. There are also powers which they share with federal government called concurrent powers. These includes maintaining courts, collecting taxes and making laws. It is important to know that there has been criticism raised in regards to federalism as federal government often interfere with the states which undermines federalsm. An example of this is Obama's Affordable Care Act (PPACA).