Matthew 10 records the call of Jesus' 12 disciples. Matthew explains that Jesus empowered them for service. The New King James Version (NKJV) says, "He gave them power." This translation might lead one to picture Jesus bestowing special "powers" on His disciples, like superheros, before sending them out to minister. We gain a clearer picture from the translation "He gave them authority" (ESV, NASB, NIV). The word is not dunamis (power, might, strength, force, capability), but exousia (state of control, potential or resource to command, control or govern). Jesus gives them the right, as His representatives, to cast out unclean spirits and heal every disease and every affliction. It is not an ability they have within themselves, but an authority that is granted to them as Jesus' personal ambassadors.
Because Jesus is the Son of God, sent from the Father and anointed by the Holy Spirit, He has the right to command the universe. Jesus grants His apostles a measure of this authority for carrying out their mission. They are to do the very works that Jesus has been doing (casting out demons, healing the sick, and proclaiming the Kingdom of Heaven). Matthew draws attention to the similarity between Jesus' ministry and that of His 12 disciples by using parallel wording to describe the activities of both Jesus and the apostles: "healing every disease and every affliction" (9:35, of Jesus); "to heal every disease and every affliction" (10:1, of the apostles).
Their identification with Jesus, which is the source of their authority, is so strong that Jesus says, "Whoever receives you receives Me, and whoever receives me receives Him who sent Me" (Matt. 10:40).
We must recognize the unique place the apostles have in the plan of redemption. They had a revelatory ministry that is unmatched by later ministers of the gospel. Their close association with Jesus as His commissioned representatives gives us confidence in their writings, as does the inspiration of the Holy Spirit.
In a similar though not identical way Jesus sends us on mission with His authority. Notice the impetus of the great commission, "All authority in heaven and on earth has been given to Me" (Matt. 28:18). When we minister "in the name of Jesus," this means (in part) that we are meeting the so-called "gods" of this world with the authority of Jesus Christ, in order to vanquish them with the Truth and advance the kingdom of Christ. "Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. An behold, I am with you always, to the end of the age" (Matt. 28:19-20).