Then Jesus summoned his twelve disciples and gave them authority over unclean spirits, to cast them out, and to cure every disease and every sickness.
Authority is a crucial concept in Christianity as we have seen in 2 Peter 2.9-10. The disciples traveled with Jesus and did not act like he did until he explicitly gave them authority to do so. They cured people because Jesus gave them authority to do so. The scribes and Pharisees demanded to know by what authority Jesus acted. At the resurrection Jesus stated that "all authority in heaven and on earth has been given to me." By whom? By the Father, obviously. The Father has given Jesus all authority everywhere. Jesus has given the disciples authority to exercise demons, cure all illnesses, make more disciples (Matthew 28.19) and even forgive the sins of people (John 20.23). Thus Jesus establishes his church with Peter and his successors at the head and the disciples and their successors under him, all with authority explicitly granted by Christ. He orders us to perpetuate this institution until he returns and states that he will be with us until the end. This presence is most evident in the Eucharist which he established and again gave authority to the disciples and their successors to perpetuate.
All civil authority comes from God as well, and is appointed by God (Romans 13.1-7) therefore we are commanded to obey it.