Why do many people feel that Federalism can be defined by examining a dollar bill and a drivers license?

Maybe federalism means the relation between the national government and the states, something that was spelled out in the Constitution in 1789. Notice that a dollar bill (representing the money circulating in the U.S.) is an example of the federal government at work, since only the federal government can issue money. Driver's licenses are issued by each state, one of the responsibilities that was left to the individual states because it was not specifically enumerated in the Constitution (naturally, since there were no cars back in those days).