One way to approach the answer to this question is to compare what the federal system of government can do that state or local governments can not. The United States Constitution clearly enumerates and differentiates the federal government from other governing bodies. Where not specifically mentioned as federal-only power, the states may assume the power to implement policy, regulation, or law, so long as it does not contradict existing federal law. I know you asked for one example, but I will provide you with three that may help you think about the answer to this question differently.
One example of federal power is the ability to wage war against foreign powers. A state can not declare war. Another example is interstate commerce. Simply explained, interstate commerce can be thought of as any economic transactions that cross state lines. For example, when a product is manufactured in one state and shipped across country, the federal government has established regulations and laws governing how the product is transported. A third example is currency. The federal system prints money and regulates the distribution of currency and the monetary system.
Without a centralized federal regulatory system, you could potentially have states declaring war, fifty different laws regarding commerce, and multiple currency systems!