What does Acts 3:9 mean?

This verse embodies the purpose Jesus gives for doing good works in public. The man in question has been healed through Peter (Act 3:1–8). In the Sermon on the Mount Jesus says:

You are the light of the world. A city set on a hill cannot be hidden. Nor do people light a lamp and put it under a basket, but on a stand, and it gives light to all in the house. In the same way, let your light shine before others, so that they may see your good works and give glory to your Father who is in heaven (Matthew 5:14–16).

The point of doing good works ought never to be to get attention for yourself (Matthew 6:1–4). Peter, John, and the other apostles have the task of bearing witness of Jesus "in Jerusalem and in all Judea and Samaria, and to the end of the earth" (Acts 1:8). The miracles they perform will help that cause. Miracles attract attention so the apostles can preach to people. And miracles validate the apostles as messengers of God. Finally, miracles bear witness that Jesus is a God of compassion and healing.

With the establishment of the canon of the New Testament, the occurrence of miracles declined. Today, God rarely chooses to heal directly as He did for the apostles. That doesn't mean that we are completely devoid of "signs" of Jesus' power. Jesus said that we prove to be His disciples if we bear much fruit (John 15:8). The fruit of the Spirit is not healing or tongues or other miracles; it is "love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control" (Galatians 5:22–23). These are characteristics of a believer who allows the Holy Spirit to work through her. In this day and age, they can be as miraculous—and rare—as a man, crippled from birth, suddenly leaping to his feet. And when such qualities catch someone's attention, we have an opportunity to bear witness to Jesus as the apostles did.