The Quorum of the Twelve Apostles: An Introduction
Lawrence R. Flake, Prophets and Apostles of the Last Dispensation (Provo, UT: Religious Studies Center, Brigham Young University, 2001), 317–19.
The word apostle literally means “one sent forth.” As the New Testament records, the Savior “chose twelve, whom also he named apostles” (Luke 6:13). The twelve disciples chosen by the resurrected Christ in ancient America were likewise ordained apostles.
In 1829, the year before the Church was organized, the Lord revealed that a latter-day Quorum of Twelve Apostles would be established. Six years later, on 14 February 1835, Joseph Smith called a meeting of the brethren who had served in Zion’s Camp. According to the direction of the Lord, the Three Witnesses to the Book of Mormon, Oliver Cowdery, David Whitmer, and Martin Harris, in consultation with the First Presidency and by inspiration, selected twelve men to become the first apostles of this dispensation. These twelve were ordained to the holy apostleship under the hands of the Three Witnesses, and then President Joseph Smith and his counselors laid their hands on them and confirmed the ordination.
Apostle is an office of the Melchizedek Priesthood, and in most cases a man ordained to this calling is also set apart as a member of the Quorum of the Twelve. One thus ordained and set apart has the sacred obligation to serve as a special witness for Jesus Christ in all the world. The question is frequently asked, “Is it necessary for a member of the Quorum of the Twelve to see the Savior in order to be an apostle?” President Joseph Fielding Smith answered in this way: “It is their privilege to see him if occasion requires, but the Lord has taught that there is a stronger witness than seeing a personage, even of seeing the Son of God in a vision. Impressions on the soul that come from the Holy Ghost are far more significant than a vision. When Spirit speaks to spirit, the imprint upon the soul is far more difficult to erase.” 
As a quorum, the Twelve are “equal in authority and power” to the quorum of the First Presidency. The following quotation from Doctrine and Covenants Commentary explains the meaning of the word “equal” in this context: “There can never be two or three quorums of equal authority at the same time; therefore in the revelation where it reads that the Twelve Apostles form a quorum equal in authority with the First Presidency, and that the Seventies form a quorum equal in authority with the Twelve, it should be understood that this condition of equality could prevail only when the ranking quorum is no longer in existence, through death or otherwise. When the First Presidency becomes disorganized on the death of the President, then the Apostles become the presiding quorum, or council, of the Church with all the power to organize again the First Presidency.” 
President of the Quorum of the Twelve
In the early history of the Quorum of the Twelve, chronological age was the basis for determining seniority, but later the criterion was changed to priority of ordination and length of continuous service. Seniority is important because although each member of the Twelve holds dormantly the priesthood keys necessary to preside over the Church, “the fulness of these keys can be exercised only in the event an apostle becomes the senior apostle of God on earth. . . . The senior apostle is always chosen and set apart as the President of the Church.” 
When the quorum of the First Presidency is organized, the apostle second in seniority is sustained as president of the Twelve. If he is called to serve as a counselor in the First Presidency, the apostle next in seniority may be sustained as Acting President of the Twelve.
It is the duty of the president of the Twelve to preside over the Quorum and to direct the ministry of its members under the leadership of the First Presidency.
 Joseph Fielding Smith, “The First Presidency and the Council of the Twelve,” Improvement Era, November 1966, 979.
 Hyrum M. Smith and Janne M. Sjodahl, Docf rine and Covenants Commentary: The Doctrine and Covenants Containing Revelations Given to Joseph Smith, Jr., the Prophet with an Introduction and Historical and Exegetical Notes, rev. ed. (Salt Lake City: Deseret Book, 1978), 700.
 Bruce R. McConkie, Mormon Doctrine, 2nd ed. (Salt Lake City: Bookcraft, 1979), 49.