When Christ ascended into Heaven He left His Apostles to lead the Church. At Pentecost the Holy Spirit arrived to guide them in their new responsibilities.
As the Church grew the Apostles started to appoint Deacons to assist them in the duties of caring for the flock. As time passed and the Church spread out geographically, the Apostles designated some of these Deacons as representatives to lead the local Church in their absence. Eventually, the Apostles designated overseers or bishops to fill their role in the expanding Church as their lives ended.
Today the fullness of the Apostolic role resides in the Bishop, who appoints priests (presbyters) and deacons to assist him and as his representatives in remote congregations.
Ignatius of Antioch, a student of John the Apostle:
Give ye heed to the bishop, that God also may give heed to you. My soul be for theirs that are submissive to the bishop, to the presbyters, and to the deacons, and may my portion be along with them in God! Labor together with one another; strive in company together; run together; suffer together; sleep together; and awake together, as the stewards, and associates, and servants of God. Please ye Him under whom ye fight, and from whom ye receive your wages. Let none of you be found a deserter. Let your baptism endure as your arms; your faith as your helmet; your love as your spear; your patience as a complete panoply. Let your works be the charge assigned to you, that ye may receive a worthy recompense. Be long-suffering, therefore, with one another, in meekness, as God is towards you.May I have joy of you for ever!
See that ye all follow the bishop, even as Jesus Christ does the Father, and the presbytery as ye would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is[administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude[of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid.