The Priesthood of Aaron is called the lesser priesthood because it is an appendage to the greater, or Melchizedek Priesthood, and has power of administering outward ordinances.
From Peter, James and John came the Melchizedek Priesthood which holds the powers, keys, and authorities to regulate the affairs of God's earthly Kingdom. These three, who were the First Presidency of the Church in their day, received the keys of the kingdom from the Savior, Moses, and Elias on the Mount of Transfiguration. (Matt. 17:1-13)
Then in June, 1829, they appeared to Joseph Smith and Oliver Cowdery and conferred upon them the following three things: 1. The Melchizedek Priesthood; 2. The keys of the kingdom of God, including the great commision to preach the gospel in all the world; and 3. The keys of the dispensation of the fulness of times. At that appearance Peter and James were resurrected beings and John was translated.
