"They arranged to meet Paul on a certain day, and came in even larger numbers to the place where he was staying." NIV translation
Because of Paul's open honesty, people were willing to listen to him and so they came in large numbers to hear what he had to say. He knew that it was the Word of God that drew people to hear and not anything about himself. Today, there is a tendency for pastors/evangelists to get a "rock star" mentality. They get carried away with themselves and forget that their whole purpose is proclaiming the gospel of Jesus Christ.
"From morning to evening he explained and declared to them the kingdom of God and tried to convince them about Jesus from the Law of Moses and from the Prophets." NIV translation
Paul met the Jews where they were in terms of their understanding. They knew of the Law of Moses and the words of the prophets and so he tried to show them that the promise of Jesus was contained in them.
This is the same thing that Jesus did with the two disciples on the Road to Emmaus after His resurrection (see Luke 24:27). The same principle applies to us in our efforts to tell people about Jesus (we must meet them where they are in their understanding).
"Some were convinced by what he said, but others would not believe." NIV translation
Paul shared the Good News and some accepted it but others did not. It is the same today but, like Paul, we are called to share the Word and trust God to open the hears of those He has chosen.
"They disagreed among themselves and began to leave after Paul had made this final statement: 'The Holy Spirit spoke the truth to your forefathers when he said through Isaiah the prophet: "Go to this people and say, 'You will be ever hearing but never understanding; you will be ever seeing but never perceiving.' For this people's heart has become calloused; they hardly hear with their ears, and they have closed their eyes. Otherwise they might see with their eyes, hear with their ears, understand with their hearts and turn, and I would heal them."'" NIV translation
Here, we see that it is possible to reach a point where you are no longer open to the work of the Holy Spirit. Paul uses this quote from Isaiah 6 and we see that the people had closed their own eyes so that they could not see the plan of God. The people could just not accept the fact that they could not work for their salvation but merely had to accept it as a gift. The same type of struggle followed Paul everywhere that he shared the good news and the same thing is happening today. This is also the same struggle that will continue even to the end of the great tribulation described in Revelation.