Federalism is a political doctrin of government which conbines a central power and the power of the minor units one by one, all at the same time. In the case of a Country, we are talking of the power of the whole State shared with the power of each providence or region simultaneously. As examples, a state responsability is always national security. A case of shared responsability between federal and state governments might be health or education issues. The constitutional amendment that gives power to the states is the Tenth, because it specifies that the proclamation of certain rights in the Constitution shall not be constructed to deny others retained by the people.
As a example laws that always varie from state to state are all that concern to traffic or the laws about permissions for carrying guns.