What does Acts 3:16 mean?

As Peter and John go to the temple to pray, they come upon a beggar who has been lame from birth. Instead of alms, Peter gives him the gift of healing (Acts 3:1–8). A crowd swarms around them as they leave the gate and settle in Solomon's Portico (Acts 3:9–11). Peter takes advantage of the attention and shows the connection between the man's healing and the people's need for Jesus.

Often, a person's faith was key to their healing. Jesus told the woman with an issue of blood, "Daughter, your faith has made you well" (Mark 5:34). But, sometimes, that faith wasn't necessary. That's certainly true for those who were raised from the dead like Lazarus (John 11:38–44) and Jairus' daughter (Mark 5:35–43). There's no reason to think Peter's mother-in-law knew what Jesus was up to (Mark 1:29–31). In this case, it appears that the faith is that of Peter. That's consistent with Mark 9:14–29. Jesus, Peter, John, and James descend the mountain after the transfiguration to find the other disciples in a struggle with a demon who has captured a little boy. Jesus doesn't condemn the boy's faith but the disciples' (Mark 9:19). Still, some will say that the man reacted to Peter's use of Jesus' name by having the faith to take Peter's hand and stand (Acts 3:6–7).

"Faith in his name" doesn't mean that Peter used the spoken words "Jesus Christ of Nazareth" as a magical spell. In the culture, one's "name" was one's reputation and character. Jesus' name includes the idea of His sovereignty, power, and authority. The healing was possible because of faith in Jesus, Himself.