The people of Israel demand a king. Up until this point in their time in Canaan, they've all lived in separate territories, but have never been united. Imagine living in America where each state is its own governing body, but there's no president.
Samuel is disappointed by the people's choice and thinks it's a reflection on him as a judge. God tells Samuel that Israel is really thinking about replacing God with a king rather than Samuel. Which makes Samuel feel better about himself, but not about the situation. We guess you can't win them all (1-9).
Samuel attempts to tell the Israelites that a king will only turn them into slaves instead of making them united. The people think this is stupid and ignore Samuel. They want a king to govern them and fight their battles, and God tells Samuel to give the people what they want and to find a king (10-22).