Like the majority of the Bible, 1 Samuel takes place in the kingdom of Israel. First called Canaan, Israel is the land of Abraham. Long story short, Abraham's descendants (Jacob and sons) moved out of Canaan, decided they wanted back in (thanks Moses) and came back. After some conquest (thanks Joshua), the Hebrews settled themselves into Canaan, eventually renaming it Israel after Jacob.
When we first start reading 1 Samuel, Israel is not a united country. The twelve tribes that make up the kingdom of Israel are divided and leaderless. They cry out to Samuel to anoint a king to unite everyone together. First comes Saul, but he stinks, so here comes David. Does he unite the kingdom?
Well, you'll have to read 2 Samuel to find out. But what's important here is that Israel needs a good king. It's a place that needs a leader more than it needs anything else. That sets the scene for David's meteoric rise to power, because we watch him, time and again, gain followers through his charisma and faith. By the time the end of 1 Samuel rolls around, the stage is set for David to take the throne and unite the twelve tribes of Israel once and for all.