What does Acts 20:20 mean?

Paul is speaking to the Ephesian elders. He is on his way to Jerusalem where he will be arrested and under house arrest for five years including two years in Rome. He will not see the Ephesians again, and he wants to remind them of important things that will help them protect their church from false teachers.

Paul doesn't have time to repeat everything he taught over the three years he lived with them, so he reminds them of himself. He doesn't do this because he's arrogant. He has planted many churches in Greece, Macedonia, and modern-day Turkey, and has watched as some of them fell into confusion and heresy because false teachers came in, repudiated him, and led the believers astray.

Paul will later similarly encourage Timothy, writing, "But as for you, continue in what you have learned and have firmly believed, knowing from whom you learned it" (2 Timothy 3:14). In Timothy's case, Paul is referring to his mother and grandmother (2 Timothy 1:5). In Galatia, Paul defended the gospel against legalistic Jews who believed Gentile Jesus-followers should first convert to Judaism (Galatians 4:9–10; 6:12–15). In Corinth, in addition to personal attacks, sects split the church as members followed different Christian leaders (1 Corinthians 1:10–17).

Paul doesn't want the Ephesian elders to follow him. He wants to remind them that his upright, self-sacrificing, devoted character reflects the authenticity and importance of his message about Jesus. That's convicting for believers now: if we're going to talk about Jesus, we need to act like Him.