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."
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 S acrament 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, though, once a married man has accepted ordination, he cannot remarry if his wife dies.
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.