He is at once separating us from Satan and making a meeting between us and the Father. Jesus' authority and power God has chosen to work through human beings. We are to share in His work of intercession, and therefore He gives to believers His authority and power. These are two important but distinct words, unfortunately muddled in the King James and a number of other translations. Authority is the right to command, act, or rule.
Power is the force or the strength needed to command, act, or rule.
We need both, but it is all too possible to have one and not the other. Sadam Hussein had the power to invade Kuwait, but he did not have the authority. The Emir of Kuwait had the authority to stop him, but no power. A traffic cop in the middle of the intersection has the authority to stop your car, but no power to do so if you choose to floor it. A thief has the power to steal your car, even though he has no authority to do so.