Paul is heartbroken at the idol worship he sees around him. Countless “gods” and “goddesses” are represented by statues and temples, and there is even one to
an “unknown God.” Paul uses this opportunity to proclaim the gospel! First he tells them that he knows this God, and this God is the one who actually made the earth and the people who inhabit it. Then he tells them that everyone longs for and searches for this God, even pointing to examples from secular poetry. He proclaims that this is the God that we need to know, and we need to repent of not knowing and following Him, because judgment is coming. But the one doing that judgment is the one who can save, and God reveals Him through the resurrection from the dead! Paul is stopped at that point. Some scoff, but some are open, and later believe.
Paul is a good example for us. While we may not consider ourselves missionaries, we have a responsibility to share our faith with those around us. Perhaps the biggest point we should take away is how Paul found some common ground, and then used that to reveal the truth about God and Jesus. Jesus did a similar thing with the woman at the well in John 4. You might want to take a look at that passage again. We should all pray that God will show us how to take the everyday and use it to reveal the supernatural!