"'God did this so that men would seek him and perhaps reach out for him and find him, though he is not far from each one of us. "For in him we live and move and have our being." As some of your own poets have said, 'We are his offspring.'" NIV translation
Did you ever wonder why God created everything? In this passage, Paul tells the Athenians the purpose. He told them that they (and we) were created to "reach out for him". All the other running after meaning and purpose is just a waste of time and a distraction from our true purpose.
"'Therefore since we are God's offspring, we should not think that the divine being is like gold or silver or stone- an image made by man's design and skill. In the past God overlooked such ignorance, but now he commands all people everywhere to repent. For he has set a day when he will judge the world with justice by the man he has appointed. He has given proof of this to all men by raising him from the dead.'" NIV translation
Now, Paul reasons with them that, if we are God's offspring (which their own poets had said), then why would we think that God is man made. He went on to remind them that God was patient with man and their lack of knowledge but that time has now passed. He then warned them of the coming judgement and gave the proof (the resurrected Jesus).
The same simple pattern applies to us today as well. Although there may be areas of the world who have never heard of Jesus, for the most part, most of the world has had the chance to hear and therefore can no longer plead ignorance. We are all called to repentance and, as Paul told the Athenians, God has set a day for judgement and given proof in the resurrection.
"When they heard about the resurrection of the dead, some of them sneered, but others said, 'We want to hear you again on this subject.' At that, Paul left the Council." NIV translation
This passage reminds us of the heart of the matter and that is the resurrection of Jesus Christ. After hearing about that, some wanted to hear more while others simply did not believe. It is the same today in that many just do not believe that Jesus was raised to life as firstfruits of the harvest of believers. After the simple message, we see that Paul "left the Council". The message of salvation through Jesus Christ is very simple.
"A few men became followers of Paul and believed. Among them was Dionysius, a member of the Aeropagus, also a woman named Damaris, and a number of others." NIV translation
In this final verse, we see that there was fruit from Paul's sharing of the Gospel in Athens. Dionysius was mentioned and we are told that he was a member of the Aeropagus so he was an educated man. He would go on to leave his family in order to share the gospel in Europe where he was beheaded for his efforts. There is not much known of Damaris as it was not the custom to keep records about women in these days. This verse can be encouraging as we see that God can reach those that are so educated but yet so lost. It seems that there are so many in this same situation today.