What does Acts 3:8 mean?

Peter has healed a lame man through the power of Jesus Christ, and the man reacts. Jews have come to the temple to pray during the evening sacrifices (Acts 3:1), and this man is leaping around. Even more, he is praising God. This is why Peter had the man look at him and know how he was healed. Peter could have mumbled a prayer while he passed the man, but he didn't. He made sure the people around them knew that the words Peter spoke healed the man.

Taken at face value, this might seem to counter Jesus' instruction in Matthew 6:2–4. Jesus explained that when you give to the poor, you should do it in secret so that you receive your reward from God and not from human witnesses. The difference in Peter's action is explained by Jesus' introduction to the instruction: "Beware of practicing your righteousness before other people in order to be seen by them" (Matthew 6:1). Peter has no intention of bringing glory to himself. He is following Jesus' words in Matthew 5:14–16: he is letting his "light shine before others, so that they may see [his] good works and give glory to [his] Father who is in heaven." In fact, once the miracle attracts the attention of the crowd, Peter immediately explains the man is healed by Jesus' power, not his own (Acts 3:11–13).

Paul will have a similar interaction with a very different result. When he and Barnabas go to Lystra and heal a crippled man, the people come to the conclusion that Barnabas is Zeus and Paul is Hermes. They even try to sacrifice to the missionaries. Paul and Barnabas insist they are not Greek gods and barely keep the priests from sacrificing to them. The tables quickly turn when critics from Antioch Pisidium and Iconium arrive. The newcomers convince the locals that not only is Paul not Hermes, he is worthy of being stoned. It is by the grace of God that Paul survives (Acts 14:8–20).