What does Acts 17:17 mean?

Paul is alone in Athens. Silas and Timothy are in Berea (Acts 17:14) and they left Luke in Philippi (Acts 17:1). Every non-Jewish city Paul has traveled to in his missionary journeys has had idols and temples, but Athens is overwhelming. Where most cities in the Roman Empire have a selection of civil gods to watch over the city, Athens seems to have collected them all—plus one, just in case (Acts 17:23). The more Paul sees, the more he feels driven to share about the true God—the only one who can save (Acts 17:16).

Fortunately, Athens is not completely foreign: there is a synagogue. Paul always starts in the synagogue (Acts 9:20; 13:13–41; 14:1; 17:1, 10; 18:4; 19:8), when there is one to be found (Acts 16:13), because the Jews and God-fearing Gentiles there have a baseline of understanding. Paul starts with the Psalms of David and the covenant God made that David would have an heir that will sit on the throne forever. He goes on to show how prophecy predicts that this heir—the Messiah—will die and rise again (Acts 13:16–41). Paul then shows how Jesus of Nazareth fulfills this prophecy: Jesus is the Messiah.

Undoubtedly, Paul also preaches in public during his different stops, but the "marketplace" of Athens is notable. It is the Agora and not only holds various merchant stalls, but also space for people to gather in assembly. It is used by noblemen to conduct business, elected officials to decide government affairs, philosophers to debate, and citizens to trade and watch entertainers. It's unclear if the people of Athens consider Paul to be a philosopher or an entertainer, but he does come to the attention of the Epicurean and Stoic philosophers. Intrigued by his teaching, and with no fear of a new God unauthorized by the Roman government, they invite him to speak at the Areopagus.