8 Then Peter, filled with the Holy Spirit, said to them: “Rulers and elders of the people! 9 If we are being called to account today for an act of kindness shown to a man who was lame and are being asked how he was healed, 10 then know this, you and all the people of Israel: It is by the name of Jesus Christ of Nazareth, whom you crucified but whom God raised from the dead, that this man stands before you healed. 11 Jesus is “‘the stone you builders rejected, which has become the cornerstone.’ 12 Salvation is found in no one else, for there is no other name under heaven given to mankind by which we must be saved.” 13 When they saw the courage of Peter and John and realized that they were unschooled, ordinary men, they were astonished and they took note that these men had been with Jesus
After Peter and John and the rest of the apostles began to do the same things that Jesus did it made the religious leaders very nervous. When they healed a man lame from birth there was unmistakable evidence that they had healed this man in Jesus' name and by His power. Peter reminds the leaders that they were the ones that rejected what the Old Testament called, "the stone the builders rejected". I bet that went over real well.
And then Peter boldly proclaims, "Salvation is found in no one else, for there is no other name under heaven given to mankind by which we must be saved." Notice the word for "saved" and "salvation" being used, which are very similar in meaning. We often misuse these words in the following ways to mean:
1. Getting forgiveness of sins
2. Escaping hell
3. Going to heaven when we die
4. Receiving eternal life
Here is how one website breaks down the biblical usage of the word "saved" as it is used in the bible.
What does the word “Saved” mean?
"To be saved means to be delivered. The vast majority of the times the word “saved” is used in Scripture, it is not used in reference to receiving eternal life or going to heaven when we die, but is used in one of these other ways mentioned above. If you doubt this, just pull out a concordance and start checking it yourself. When the Bible uses the word “saved” it is talking about the Israelites getting saved from their enemies, from sickness, from slavery, and from death. The disciples are saved from drowning in a storm. Christians can be saved from a life of empty living."
So we see in this context Peter is referring to the deliverance of the man from being physically lame. And Peter is saying that there is no other name in which they could provide this healing/deliverance than Jesus. Since the leaders were trying to downplay the movement Jesus had just started, you can see why there were so very worried. But at the same time all the people saw this man before and after they prayed for him. He was clearly healed, so how could they deny that?
When we pray for people and they are delivered from anything harmful in their lives, it reflects the power and authority we have in Jesus' name. People can argue with what we say, but can't argue with results right in front of them. This is why I believe that God is still active working through his disciples to do the same things Jesus did including healing and delivering the sick. We as Jesus' disciples can continue to prove that Jesus is the only name under which we might be saved!