The Pharaoh (FARE-oh) owned all of Egypt, and everything in it: all the land, all the tools, all the animals, and all the people. He or she could tell anybody what to do, and they would have to do it. The Egyptian government was a monarchy. Of course the Pharaoh could not always be telling everybody what to do. So the Pharaohs chose people to represent them, and assigned the people to big estates all over Egypt. These rich men and women ran the estates, and on them they could tell everybody what to do. But even the rich people were supposed to do whatever the Pharaohs said to do, and they had to send the Pharaohs some of the food that was grown on that land. Some, at least, of these estate-holders were priests, holding the estate for the gods, but these religious estates were run in the same way, and they also had to pay some food to the Pharaohs.
When the Pharaohs were weaker, especially in the First and Second Intermediate Periods, sometimes they could not make the rich people do what they wanted them to. Often the Pharaoh had to compromise with the rich people. But at least in theory, the rich people had to do whatever the Pharaoh said, and ordinary people had to do whatever the rich people said.
To find out more about Egyptian government, check out these books from Amazon.com or from your library:
Eyewitness: Ancient Egypt, by George Hart. For kids.
Politics and Government in Ancient Egypt, by Leslie Kaplan (2004). For kids.
Everyday Life in Ancient Egypt, by Lionel Casson (revised edition 2001). Not especially for kids, but pretty entertaining reading, and Casson knows what he's talking about.