What does Acts 17:22 mean?
Athens is the site of a court called the Areopagus on the top of a rock outcropping. Paul has been aggressively invited to share his religious views there, by Epicurean and Stoic philosophers who heard him preaching in the Agora. We only have recordings of two of Paul's sermons. In Acts 13, he is in a synagogue in Pisidian Antioch, surrounded by Jews and God-fearing Gentiles who are dedicated to studying the Jewish Scriptures—our Old Testament—including the prophecies. He moves quickly through Jewish history to David and God's covenant that the Messiah would come through David's line. He then reminds them that John the Baptist identified the Messiah as Jesus of Nazareth. The crux of his message is that the prophets—including David—said that the Messiah would die and be raised again, as Jesus was (Acts 13:16–41).The Athenian philosophers likely know little about Jewish prophecy and have no interest in this Messiah, so Paul uses what they do know. When he arrived, he noticed the city was filled with idols (Acts 17:16)—so many they had an altar to an unknown god, just in case they missed somebody (Acts 17:23). Paul quickly dismisses the pantheon and shows how the classical poets recognize a single Creator God. Paul branches from this point of contact to say the Creator God has a representative who will judge the dead and who Himself died and rose again (Acts 17:21–31).
"Very religious" is from the Greek root word deisidaimōn which can mean pious or superstitious. He is literally talking about all the idols, but Paul is not above being a little sarcastic. His words might be a slight since Stoics were very logical and Epicureans were likely actually atheists. It was also against form to flatter one's audience at the Areopagus to win approval of an argument.
Some scholars say Paul's decision to try to reach the people through their own culture instead of presenting a clear gospel message is why only a handful of people believe (Acts 17:34). They say Paul realizes his mistake and when he reaches Corinth preaches only "Jesus Christ and him crucified" (1 Corinthians 2:1–2) as a result. Others say he is being missional by directly addressing the evil in the culture—idolatry—and that without his culture-spanning approach, even fewer would have responded.