For a deeper summary look into scriptural reference of the Melchizedek History, please visit Melchizedek Priesthood Power and Christ.
Among the Latter-day Saints, the priesthood is considered to be the power and authority of God, including the authority to act as a leader in the church and to perform ordinances, and the power to perform miracles. A body of priesthood holders is referred to as a quorum.
Priesthood denotes elements of both power and authority. The priesthood includes the power Jesus gave his apostles to perform miracles such as the casting out of devils and the healing of sick (Luke 9:1). Latter Day Saints believe that the Biblical miracles performed by prophets and apostles were performed by the power of priesthood, including the miracles of Jesus, who holds all of the keys of the priesthood.
The priesthood is formally known as the Priesthood after the Order of the Son of God, but to avoid the too frequent use of the name of the Son of God, the priesthood is referred to as the Melchizedek Priesthood, Melchizedek being the high priest to whom Abraham paid tithes.
This priesthood is the authority by which a bearer may perform ecclesiastical acts of service in the name of God. Latter Day Saints believe that acts (and in particular, ordinances) performed by one with priesthood authority are recognized by God and are binding in heaven, on earth, and in the afterlife. In addition, Latter Day Saints believe that leadership positions within the church are legitimized by the priesthood authority.