Rome wasn't always a powerful empire: This history tells how that rise to power came to be. (The vast majority of the document is lost, so this is the summary of what remains.)
The history tells first of Rome from before Polybius's time, from what he has learned from the elderly folks of yesteryear. He details the longterm annexation and conquering of Carthage. This allowed Rome a kind of foothold through which they then conquered the whole of Greece. He details political business among nearby nations: the Egyptians, and the Macedonians.
He tells of the Punic Wars. About the First Punic War, we learn more about Carthage as a region, and the importance of Rome's conquering it in the years 264-241 BC. This allowed Rome a kind of absolute control of the Mediterranean, so they could trade with Northern Africa from the capitol in Italy. The Second Punic War tells of Hannibal, the military genius who crossed the whole of Europe to invade Rome from the north, famously crossing the Alps to do so. In the Third Punic War, Rome's empire has become obvious.
Then, Polybius discusses the current state of his democracy: He mentions taxation, voting, aristocracy, and the reality of power as a shared resource. He discusses the value of the Senate and the various strategies that the Senate employs to create balance in the government. The history ends with Polybius's telling of the fall of Corinth to the Romans in 146 BC.