The Sacrament of Holy Orders is the continuation of Christ's priesthood, which He bestowed upon His Apostles; thus, the Catechism of the Catholic Church refers to the Sacrament of Holy Orders as "the sacrament of apostolic ministry."
"Ordination" comes from the Latin word ordinatio, which means to incorporate someone into an order. In the Sacrament of Holy Orders, a man is incorporated into the priesthood of Christ, at one of three levels: the episcopate, the priesthood, or the diaconate.
The priesthood was established by God among the Israelites during their exodus from Egypt. God chose the tribe of Levi as priests for the nation. Their primary duties were the offering of sacrifice and prayer for the people.
Christ, in offering Himself up for the sins of all mankind, fulfilled the duties of the Old Testament priesthood once and for all. But just as the Eucharist makes that sacrifice present to us today, so the New Testament priesthood is a sharing in the eternal priesthood of Christ. While all believers are, in some sense, priests, some are set aside to serve the Church as Christ Himself did.
There is only one Sacrament of Holy Orders, but there are three levels. The first is that which Christ Himself bestowed upon His Apostles: the episcopate. A bishop is a man who is ordained to the episcopate by another bishop (in practice, by several bishops). He stands in a direct, unbroken line from the Apostles, a condition known as "apostolic succession."
Ordination as a bishop confers the grace to sanctify others, as well as the authority to teach the faithful and to bind their consciences. Because of the grave nature of this responsibility, all episcopal ordinations must be approved by the Pope.
The second level of the Sacrament of Holy Orders is the priesthood. No bishop can minister to all of the faithful in his diocese, so priests act, in the words of the Catechism of the Catholic Church, as "co-workers of the bishops." They exercise their powers lawfully only in communion with their bishop, and so they promise obedience to their bishop at the time of their ordination.
The chief duties of the priesthood are the preaching of the Gospel and the offering of the Eucharist.
The third level of the Sacrament of Holy Orders is the diaconate. Deacons assist priests and bishops, but beyond the preaching of the Gospel, they are granted no special charism or spiritual gift.
In the Eastern Churches, both Catholic and Orthodox, the permanent diaconate has been a constant feature. In the West, the office of deacon was reserved to men who intended to be ordained to the priesthood. The permanent diaconate was restored in the West by the Second Vatican Council. Married men are allowed to become permanent deacons.
The Sacrament of Holy Orders can be validly conferred only on baptized men, following the example set by Christ and His Apostles, who chose only men as their successors and collaborators. A man cannot demand ordination; the Church has the authority to determine eligibility for the sacrament.
While the episcopate is reserved to unmarried men, the discipline regarding the priesthood varies in East and West. The Eastern Churches allow married men to be ordained priests, while the Western Church insists on celibacy. Once a man has received the Sacrament of Holy Orders, however, he cannot marry.
As the Catechism of the Catholic Church notes:
The essential rite of the sacrament of Holy Orders for all three degrees consists in the bishop's imposition of hands on the head of the ordinand and in the bishop's specific consecratory prayer asking God for the outpouring of the Holy Spirit and his gifts proper to the ministry to which the candidate is being ordained.
Other elements of the sacrament, such as holding it in the cathedral (the bishop's own church); holding it during Mass; and celebrating it on a Sunday are traditional but not essential.
Because of his role as a successor to the Apostles, who were themselves successors to Christ, the bishop is the proper minister of the sacrament. The grace of sanctifying others that he receives at his own ordination allows him to ordain others.
The Sacrament of Holy Orders, like the Sacrament of Baptism and the Sacrament of Confirmation, can only be received once for each level of ordination. Once a man has been ordained, he is spiritually changed, which is the origin of the saying, "Once a priest, always a priest." He can be dispensed of his obligations as a priest (or even forbidden to act as a priest); but he remains a priest forever.
Each level of ordination confers special graces, from the ability to preach, granted to deacons; to the ability to act in the person of Christ to offer the Mass, granted to priests; to a special grace of strength, granted to bishops, which allows him to teach and lead his flock, even to the point of dying as Christ did.