Origin 50 to 250 CE
A priest is authorised to do what no one else in the church may do. The decisive act is ordination by a bishop through the laying on of hands, which Catholic and Orthodox teaching holds to confer a permanent character. A priest who is laicised, suspended, or leaves in disgrace remains, in the church's own accounting, a priest; the sacraments he confers afterwards are valid though unlawful. What ordination authorises is the consecration of the Eucharist, absolution in confession, and the anointing of the sick. A layperson who says the words of consecration over bread has not performed an invalid sacrament, but no sacrament at all. Baptism is the exception that shows where the line falls: anyone at all, including an unbeliever, may baptise in an emergency, and the church counts it.
The office is for life. In the Latin Church it carries a promise of celibacy, which is a discipline and not a doctrine, which is why Eastern Catholic and Orthodox churches ordain married men without any difficulty of principle, though a married priest may not become a bishop and a widowed priest may not remarry.
Ordination is restricted to men in the Catholic and Orthodox churches. Rome's position was stated in Inter Insigniores in 1976 and again in Ordinatio Sacerdotalis in 1994, which declared the church has no authority to ordain women; whether that declaration is infallible is itself argued about by Catholic theologians. Most provinces of the Anglican Communion now ordain women as priests and many as bishops; others do not, and provinces in communion with one another disagree openly. This is a live disagreement, not a settled question, and it has produced parallel structures inside single churches.