What does Luke 9:1 mean?
In Luke 9:1–6, Jesus empowers the disciples to "heal the sick, raise the dead, cleanse lepers, [and] cast out demons" (Matthew 10:8). This is the first time the disciples take an active role in the ministry for which Jesus is training them. All but cleansing lepers reflect the last three miracles of Jesus that Luke recounts (Luke 8:26–56); Luke mentioned Jesus cleansing a man of leprosy earlier (Luke 5:12–16). Jesus gives them this power to ease the pain of those who are struggling, but also to validate their proclamation of the kingdom of God (Luke 9:2)"The Twelve" are the twelve primary disciples Jesus chose early in His ministry (Luke 6:12–16). Often, Jesus travels with many more than just these (Luke 8:1–3, 9). Soon, Jesus will empower seventy-two of His followers to preach and perform miracles (Luke 10:1–12).
"Power" doesn't mean that the disciples are somehow given superpowers to use as they please. Jesus gave them very specific ability to do what He wants them to do: heal people and expel demons. "Authority" is translated from a Greek term implying a resource or power one has the right to control. As in English, "power" is the raw ability to do something, while "authority" is the right to do it. Matthew 10:1 and Mark 6:7 use "authority" as representative of both.