What is priesthood?

Answer 1

Priest is one who offers sacrifice to God, under the Old Covenant the chosen people were constituted by God as "a kingdom of priests and a holy nation." (Exodus 19:6; cf. Isaiah61:6). Then the tribe of Levi was set apart for liturgical service. As Hebrews says (Heb 5:1; cf. Exodus 29:1-30; Lev 8) the priests are "appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for sins."

These, along with the high priest, Melchizedek (Heb 5:10; Gen 14:18) were the prefiguring of the New Testament priest, the Son of God, who came and offered the "one perfect sacrifice" - Himself, to God the Father on our behalf. This redemptive sacrifice is unique, and accomplished once for all, yet as Christ is God, and outside of time, so is His Sacrifice of Himself, so that sacrifice is re-presented in every holy Eucharist, enabling all people, everywhere, and throughout time, to witness His One Sacrifice for the forgiveness of their sins.

To that end, He has instituted priests in His Church--the ministerial priesthood, which is at the service of the common priesthood, that of all believers. Thus "priesthood" refers usually to the ministerial priesthood who stands in the person of Christ before the altar and offers the sacrifice of Calvary to the Father on our behalf. The priesthood, thus, comprises all of those men who are ordained in the apostolic succession by the Bishop as a priest of God.

from Modern Catholic Dictionary by John A. Hardon, S.J. Doubleday & Co., Inc. Garden City, NY 1980

Priest. An authorized mediator who offers a true sacrifice in acknowledgment of God's supreme dominion over human beings and in expiation for their sins. A priest's mediation is the reverse of that of a prophet, who communicates from God to the people. A priest mediates from the people to God.

Christ, who is God and man, is the first, last, and greatest priest of the New Law. He is the eternal high priest who offered Himself once and for all on the Cross, a victim of infinite value, and he continually renews that sacrifice on the altar through the ministry of the Church.

Within the Church are men who are specifically ordained as priest to consecrate and offer the body and blood of Christ in the Mass. The Apostles were the first ordained priests, when on Holy Thursday night Christ told them to do in his memory what he had just done at the Last Supper. All priests and bishops trace their ordination to the Apostles. Their second essential priestly power, to forgive sins, was conferred by Christ on Easter Sunday, when he told the Apostles, "For those whose sins you forgive, they are forgiven; for those whose sins you retain, they are retained: (John 20-22, 23). All the Christian faithful, however, also share in the priesthood by their baptismal character. They are enabled to offer themselves in sacrifice with Christ through the Eucharistic liturgy. They offer the Mass in the sense that they internally unite themselves with the outward offering made by the ordained priest alone.

Answer 2

its quite similar as the priesthood of the faithful. Its when the priests become ordained and are consecrated to now serve the body of Christ. Hope this satisfies your question!