"Some Jews who went around driving out evil spirits tried to invoke the name of the Lord Jesus over those who were demon-possessed. They would say, 'In the name of Jesus, whom Paul preaches, I command you to come out.'" NIV translation
When some Jews saw what God was doing through Paul, they decided that they could do the same thing by using the name of Paul. This is a good example of people trying to walk under the umbrella of another's anointing. The problem with this is that it forgets the main thing which is that all gifts (anointings) come from God and are given by His grace to those He chooses. We cannot live on someone else's faith and walk our personal walk with the Lord.
"Seven sons of Sceva, a Jewish chief priest, were doing this. One day, the evil spirit answered them, 'Jesus I know, and I know about Paul, but who are you?' Then the man who had the evil spirit jumped on them and overpowered them all. He gave them such a beating that they ran out of the house naked and bleeding." NIV translation
Now, Paul gives us an example of what happens when a person tries to live on someone else's faith. The sons of the high priest did not know Jesus yet were trying to harness the power of God. It did not work for them and it will not work for us. The man with the demon ended up beating the seven men and they must have been embarassed as they ran out naked and bloody. It is a strong warning for us as well in that, if we do not want similar results, we must have the right relationship with the Father through the Son so we can be empowered of the Spirit. Then and only then, will the evil spirits be cast out.
"When this became known to the Jews and Greeks living in Ephesus, they were all seized with fear, and the name of the Lord Jesus was held in high honor." NIV translation
When the word got out that the demons knew Jesus and retreated at His name, the people lifted up the name of Jesus in honor. The power of God was demonstrated and people began to fear Him and that is why God empowers his people to do miraculous things. He does not want us to use our spiritual gifts like a magic show as everything must be done for His glory and not our own.
"Many of those who believed now came and openly confessed their evil deeds. A number who had practiced sorcery brought their scrolls together and burned them publicly. When they calculated the value of the scrolls, the total came to fifty thousand drachmas. In this way the word of the Lord spread widely and grew in power." NIV translation
Fear causes change in people and, when they saw what was happening, they turned from their evil ways (repented) and even burned the detestable things that were a part of their job. These people that practiced sorcery earned their living that way but they gave it up and even burned their scrolls which were the tools they used to make a living. When people saw genuine repentance and obedience, word spread rapidly! This same pattern is true for us today as, when we come to Christ, we are also called to openly confess our sins and to turn from them (repent) even if that is how we earn a living. The Lord takes care of His own!