And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades shall not prevail against it. And I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven. Matthew 16:18-19
During Jesus's ministry the Apostles were granted the authority to do much of what Christ did like healing the sick and preaching about the Kingdom. After the Resurrection, Christ invested the Apostles with even more authority. In John 20, Christ breathes on the Apostles and grants them the authority to forgive sins. He also unites the Apostles with the same mission that Christ was given when He says, "As the Father has sent me, I am sending you." The Apostles are granted authority over the church when they are given the power "to bind and loose". From the beginning of their ministry, the Apostles's were made hierarchal leaders of the Church Christ was building.
As the Church grew, the Apostles recognized the need for help with the inner workings of their ministry. For this purpose the Apostles chose 7 deacons. The Apostles would travel from city to city sharing the Gospel and starting churches. They would appoint elders in these churches and the elders would be subject to the Apostles teaching as evidenced by the council in Jerusalem in Acts 15. The council made a ruling and that ruling was delivered to all the churches who were expected to honor the ruling.
In 2 Timothy 4:14 we learn that Timothy is now considered an Apostle. We also learn that Timothy was given this gift by the laying on of hands from the elders. In 2 Timothy 1:6 we discover that Paul was one of those elders. When the Apostles granted authority to new elders, it was expected that those elders would do the same to someone else. In 1 Timothy 3: 1-13, Paul gives Timothy a list of requirements when selecting a bishop or deacon to aid in the decision and in 1 Timothy 5:22, Paul tells Timothy not to be hasty in laying on hands. We can gather from these verses that Timothy is expected to select new elders just as Paul had selected him. This task is done by the laying on of hands and is something to be taken seriously. The pattern that forms is God granting Paul authority, then Paul granting Timothy authority and this is expected to continue in a line of succession. The Church defines this teaching as Apostolic Succession.
As the church expanded so would its hierarchical structure, still based on the earlier example of the Apostles but at a larger scale consisting of Bishops, Priests, and Deacons.
Bishops are the leading members of the church and are responsible to insure the truth and the unity of the faith. Bishop comes form the Greek word Episkopos meaning overseer. No bishop is over another bishop, nor is he over the congregation, but a member of it. Bishops oversee a particular geographic area called a diocese. A bishop in the main city of an area with many dioceses is called the metropolitan or archbishop. A bishop in the capital city or an area containing other metropolitanates and dioceses is known as the Patriarch. The Patriarch is given a great deal of respect, but is not over the bishop of a diocese. All bishops are identical and equal in church authority.
Priests also known as presbyters, assist the bishop in ecclesiastical work in the diocese. Priests are assigned by, and are an extension of, the Bishop to serve at a specific parish where he is to take care of the spiritual needs of that community. When the Church was smaller this was done by the Bishop, but now the Priest is given a blessing to do so. A priest must be ordained by a Bishop.
The authority that is granted to a bishop is passed on from one bishop to another. This authority is the same that was given to the Apostles as well as those chosen by the Apostles via the laying on of hands.
According to Hebrews 13:17, we are to "Obey those who rule over you, and submit to their authority, for they watch out for your souls, as those who must give account." That is our relationship with the elders of the church. We submit to their authority and they in turn watch out for our souls.