Final answer:
A system that grants significant power to local governments within a country is known as federalism, which establishes multiple levels of government with autonomous authority as provided by the national constitution.
Step-by-step explanation:
A system that allocates strong power to units of local government within a country is called a federalism. A federal system creates two relatively autonomous levels of government, each possessing authority granted to them by the national constitution.
This style of governance is often chosen when a country contains multiple national identities or when it is still in the process of nation-building. In contrast to federalism, a unitary system makes subnational governments dependent on the national government, where significant authority is centralized.
However, some nations have evolved from a strictly unitary system to a more decentralized structure through a process of devolution, granting more power and responsibilities to regional governments.