This form of government is defined in Wikipedia¹ as:

“A federation (also known as a federal state) is a political entity characterized by a union of partially self-governing states or regions under a central (federal) government. In a federation, the self-governing status of the component states, as well as the division of power between them and the central government, is typically constitutionally entrenched and may not be altered by a unilateral decision of either party, the states or the federal political body. Alternatively, federation is a form of government in which sovereign power is formally divided between a central authority and a number of constituent regions so that each region retains some degree of control over its internal affairs.”

The most notable examples of this form today are the United States, Australia, Canada, Germany, India, Mexico and Russia.

---

1. Wikipedia is NOT my go to source but for something this basic, it’s the quickest. I will NOT make a habit of this on the site.