What does Mark 3:15 mean?
Casting out demons is a significant part of Jesus' ministry. It shows compassion for people who are suffering, but also validates that His teaching is of God. The apostles' authority is partially dependent on their faith. In Mark 9:14–29, the disciples are unable to free a boy from demonic possession. Jesus first scolds the disciples for their lack of faith, and then tells them that some demons can only be expelled by prayer.It is unclear how big a part demon exorcism is meant to play in modern evangelism. A conservative view is preferable because of the very real threat of abuse. Too many Christian circles consider every illness, sin, and run of bad experiences to be caused by direct demonic involvement. It is abuse to subject people to "exorcisms" when they have a very real need of doctors, counselors, or just job training. We can functionally "cast out demons" without exorcising. Speaking truth does very real damage to Satan's work. Truth will free people from bonds of sin—both their own and others (John 8:31–32).
Authority, from the Greek root word exousia, means to have the power to make decisions for oneself or others. God has authority over us because He made us (Romans 9:21). Eventually, the disciples will allow God's power to move through them in a way that gives them power to choose what demons will do (Acts 16:16–18).