For Catholics, ordination is a sacrament. Through ordination, a man becomes a priest, his priesthood indelibly imprinted on his soul, forever. Although many Christians feel that the priesthood ended with Christ, Catholics see the Levitical priesthood as a prefiguring of the ordained ministry of the New Covenant. As the Catholic Catechism explains:
This is important to note in the face of the accusation that Catholic priests are usurping the place Christ, who is our only true priest.
1544 Everything that the priesthood of the Old Covenant prefigured finds its fulfillment in Christ Jesus, the "one mediator between God and men." The Christian tradition considers Melchizedek, "priest of God Most High," as a prefiguration of the priesthood of Christ, the unique "high priest after the order of Melchizedek"; "holy, blameless, unstained," "by a single offering he has perfected for all time those who are sanctified," that is, by the unique sacrifice of the cross.
1545 The redemptive sacrifice of Christ is unique, accomplished once for all; yet it is made present in the Eucharistic sacrifice of the Church. The same is true of the one priesthood of Christ; it is made present through the ministerial priesthood without diminishing the uniqueness of Christ's priesthood: "Only Christ is the true priest, the others being only his ministers."
The Catholic Church does recognize the priesthood of all believers, or baptismal priesthood. The role of the ordained priesthood is to serve the rest of us, through dispensing the sacraments.
1120 The ordained ministry or ministerial priesthood is at the service of the baptismal priesthood. The ordained priesthood guarantees that it really is Christ who acts in the sacraments through the Holy Spirit for the Church. The saving mission entrusted by the Father to his incarnate Son was committed to the apostles and through them to their successors: they receive the Spirit of Jesus to act in his name and in his person. The ordained minister is the sacramental bond that ties the liturgical action to what the apostles said and did and, through them, to the words and actions of Christ, the source and foundation of the sacraments.
But how does the ordained priesthood have the authority to marry people, to forgive sins, etc? They were given this authority by Jesus, as it was passed down through the apostles.
And Moses said, Hereby ye shall know that the LORD hath sent me to do all these works; for I have not done them of mine own mind. Num 16:28
God gives Moses the authority to perform works on his behalf.
I can of mine own self do nothing: as I hear, I judge: and my judgment is just; because I seek not mine own will, but the will of the Father which hath sent me. John 5:30
In the same way, Jesus, as a man, acts under the authority of the Father.
And I appoint unto you a kingdom, as my Father hath appointed unto me Luke 22:29
Then he called his twelve disciples together, and gave them power and authority over all devils, and to cure diseases. Luke 9:1
Jesus gives this authority to his disciples.
And with that he breathed on them and said, "Receive the Holy Spirit." John 20:22
God imparted life to Adam through breathing on him. Therefore, this breathing was not just a symbol, but a sacrament. An outward sign of an inward grace which they received. This is something which they knew would be passed on to those who would come after them.
Acts 1:20-26 For it is written in the book of Psalms, Let his habitation be desolate, and let no man dwell therein: and his bishoprick let another take. Wherefore of these men which have companied with us all the time that the Lord Jesus went in and out among us, Beginning from the baptism of John, unto that same day that he was taken up from us, must one be ordained to be a witness with us of his resurrection. And they appointed two, Joseph called Barsabas, who was surnamed Justus, and Matthias. And they prayed, and said, Thou, Lord, which knowest the hearts of all men, shew whether of these two thou hast chosen, That he may take part of this ministry and apostleship, from which Judas by transgression fell, that he might go to his own place. And they gave forth their lots; and the lot fell upon Matthias; and he was numbered with the eleven apostles.
As this article from This Rock explains, "Peter considers Judas’s betrayal as a fulfillment of Old Testament prediction. And he also quotes from the Greek Septuagint translation of Psalm 109:8 (Psalm 108:8 in the Septuagint numbering) to show that filling the office was foreseen in Scripture. Verse 20 reads, "His office let another take." The word translated "office" is episkope, which in New Testament language means "episcopal office" (see 1 Tim. 3:1)."
Acts 9:7 shows that even Paul was ordained before he begins his ministry. And Ananias went his way, and entered into the house; and putting his hands on him said, Brother Saul, the Lord, even Jesus, that appeared unto thee in the way as thou camest, hath sent me, that thou mightest receive thy sight, and be filled with the Holy Ghost. Paul sees this ministry being passed down through the generations, "And the things that thou hast heard of me among many witnesses, the same commit thou to faithful men, who shall be able to teach others also." (2 Tim. 2:2).
So, the apostles received this authority from Jesus, which they passed down to their successors, which they passed down through the generations, and which we still recognize today, as do a few other churches. The Catechism explains it in this way:
1562 "Christ, whom the Father hallowed and sent into the world, has, through his apostles, made their successors, the bishops namely, sharers in his consecration and mission; and these, in their turn, duly entrusted in varying degrees various members of the Church with the office of their ministry." "The function of the bishops' ministry was handed over in a subordinate degree to priests so that they might be appointed in the order of the priesthood and be co-workers of the episcopal order for the proper fulfillment of the apostolic mission that had been entrusted to it by Christ."
1563 "Because it is joined with the episcopal order the office of priests shares in the authority by which Christ himself builds up and sanctifies and rules his Body. Hence the priesthood of priests, while presupposing the sacraments of initiation, is nevertheless conferred by its own particular sacrament. Through that sacrament priests by the anointing of the Holy Spirit are signed with a special character and so are configured to Christ the priest in such a way that they are able to act in the person of Christ the head."
1564 "Whilst not having the supreme degree of the pontifical office, and notwithstanding the fact that they depend on the bishops in the exercise of their own proper power, the priests are for all that associated with them by reason of their sacerdotal dignity; and in virtue of the sacrament of Holy Orders, after the image of Christ, the supreme and eternal priest, they are consecrated in order to preach the Gospel and shepherd the faithful as well as to celebrate divine worship as true priests of the New Testament."
1565 Through the sacrament of Holy Orders priests share in the universal dimensions of the mission that Christ entrusted to the apostles. The spiritual gift they have received in ordination prepares them, not for a limited and restricted mission, "but for the fullest, in fact the universal mission of salvation 'to the end of the earth," "prepared in spirit to preach the Gospel everywhere."
1566 "It is in the Eucharistic cult or in the Eucharistic assembly of the faithful (synaxis) that they exercise in a supreme degree their sacred office; there, acting in the person of Christ and proclaiming his mystery, they unite the votive offerings of the faithful to the sacrifice of Christ their head, and in the sacrifice of the Mass they make present again and apply, until the coming of the Lord, the unique sacrifice of the New Testament, that namely of Christ offering himself once for all a spotless victim to the Father." From this unique sacrifice their whole priestly ministry draws its strength.
1567 "The priests, prudent cooperators of the episcopal college and its support and instrument, called to the service of the People of God, constitute, together with their bishop, a unique sacerdotal college (presbyterium) dedicated, it is, true to a variety of distinct duties. In each local assembly of the faithful they represent, in a certain sense, the bishop, with whom they are associated in all trust and generosity; in part they take upon themselves his duties and solicitude and in their daily toils discharge them." priests can exercise their ministry only in dependence on the bishop and in communion with him. The promise of obedience they make to the bishop at the moment of ordination and the kiss of peace from him at the end of the ordination liturgy mean that the bishop considers them his co-workers, his sons, his brothers and his friends, and that they in return owe him love and obedience.
1568 "All priests, who are constituted in the order of priesthood by the sacrament of Order, are bound together by an intimate sacramental brotherhood, but in a special way they form one priestly body in the diocese to which they are attached under their own bishop. . . ." The unity of the presbyterium finds liturgical expression in the custom of the presbyters' imposing hands, after the bishop, during the rite of ordination.
Our records of the early church attest to their belief in apostolic succession.
"Through countryside and city [the apostles] preached, and they appointed their earliest converts, testing them by the Spirit, to be the bishops and deacons of future believers. Nor was this a novelty, for bishops and deacons had been written about a long time earlier.... Our apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry." (Clement of Rome, Epistle to the Corinthians 42:4-5, 44:1-3 [A.D. 80]).
"Polycarp also was not only instructed by apostles, and conversed with many who had seen Christ, but was also, by apostles in Asia, appointed bishop of the church in Smyrna, whom I also saw in my early youth, for he tarried [on earth] a very long time, and, when a very old man, gloriously and most nobly suffering martyrdom, departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true. To these things all the Asiatic churches testify, as do also those men who have succeeded Polycarp down to the present time" (Irenaeus, Against Heresies 3:3:4). A.D. 189]
"[I]t is incumbent to obey the presbyters who are in the Church—those who, as I have shown, possess the succession from the apostles; those who, together with the succession of the episcopate, have received the infallible charism of truth, according to the good pleasure of the Father. But [it is also incumbent] to hold in suspicion others who depart from the primitive succession, and assemble themselves together in any place whatsoever, either as heretics of perverse minds, or as schismatics puffed up and self-pleasing, or again as hypocrites, acting thus for the sake of lucre and vainglory. For all these have fallen from the truth" (Irenaeus, Against Heresies, 4:26:2).
"But if there be any [heresies] which are bold enough to plant [their origin] in the midst of the apostolic age, that they may thereby seem to have been handed down by the apostles, because they existed in the time of the apostles, we can say: Let them produce the original records of their churches; let them unfold the roll of their bishops, running down in due succession from the beginning in such a manner that [their first] bishop shall be able to show for his ordainer and predecessor some one of the apostles or of apostolic men—a man, moreover, who continued steadfast with the apostles. For this is the manner in which the apostolic churches transmit their registers: as the church of Smyrna, which records that Polycarp was placed therein by John; as also the church of Rome, which makes Clement to have been ordained in like manner by Peter" (Tertullian Demurrer Against the Heretics 32 [A.D. 200].