The priesthood was established by God among the Israelites during their exodus from Egypt. God chose the tribe of Levi as priests for the Hebrew nation. The primary duties of the priests were the offering of sacrifice and prayer for the people.
Jesus 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 Christ’s 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.