What does Acts 19:15 mean?

Paul is in Ephesus. As part of his ministry, he is using the power of the Holy Spirit and the authority of Jesus to heal people and expel demons. This shows legitimate power in a city filled with witchcraft and charlatans. Other Jews are there, as well, using the mystery of the invisible God of Judaism to enchant the Gentile residents who suffer under demonic oppression.

The sons of Sceva claim their father is a Jewish high priest. It's unclear if this is true. They, like many other Jews, watch Paul exorcise demons with Jesus' name and attempt to do the same. During Jesus' ministry, He and the disciples met a man using Jesus' name although he wasn't a disciple. The disciples wanted him to stop, but Jesus told them to leave him alone. The man may not have been Jesus' follower, but he had a sincerity that caused no harm to Jesus' mission (Mark 9:38–41).

The sons of Sceva, however, don't seem to realize just using Jesus' name doesn't give the exorcist unlimited power. Even the disciples learned this when they tried to expel the demon from the boy (Mark 9:14–29). The Jewish exorcists are not authorized to use the name of Jesus because they don't know Him.

The demon reacts to the name of Paul because it knows Paul has the power of Jesus. It reacts to the name of Jesus because it knows Jesus is the Son of God (Mark 1:24–25; 3:11–12; 5:7). But even though the exorcists say the sounds that people use to refer to the man Jesus, they don't know the name of Jesus: His power, authority, and sovereignty. To the demon, the sons of Sceva have "the appearance of godliness, but [deny] its power" (2 Timothy 3:5).