Final answer:
The fundamental division of authority between the national government and the state governments is known as federalism, which allows for power-sharing and the preservation of state rights within the U.S. governmental structure.
Step-by-step explanation:
The fundamental division of authority between the national government and the fifty state governments is known as federalism. This system is a Constitutional framework that ensures the division and power-sharing between the national and state governments. Federalism is essential to the U.S. government as it provides a balance, preventing any single entity from holding too much power. In this system, each level of government has certain powers and responsibilities that are unique to them, and some that are shared. The concept is deeply rooted in the desire to preserve the rights of states and their citizens, allowing for a multitude of "laboratories" in which different government systems and policies can be tried and tested.
Different aspects of the governmental structure such as separation of powers and checks and balances ensure that different branches of government can limit each other's power, thereby requiring cooperation to govern effectively. However, the division of sovereignty between the national government and the states is the defining characteristic of federalism.