From the account in 2 Kings 2:1-18, about Elisha taking up Elijah's prophetic mantle, the word mantle has come to symbolize the authority that rests upon the Lord's anointed who presides over His Church at any given time.
President Spencer W. Kimball, then president of the Quorum of the Twelve and speaking at the Weber State College Institute of Religion on March 29, 1973, told of how he had witnessed that prophetic mantle fall on three men who served successively as president of the Church."President [David O.] McKay had been a man among men, a great prophet and a great leader, and a counselor to two Church presidents, but now after he was ordained and set apart as the President of the Church, I saw him rise to new pinnacles of power and authority and effectiveness," President Kimball recounted. "He began to speak with the voice of authority. The inspiration that came from him was contagious. His pronouncements were mature and all-encompassing. His leadership showed that unmistakably the mantle of his calling was upon him.
"I saw the mantle pass again when on the day following the funeral of President David O. McKay, President Joseph Fielding Smith was elevated to the first place. When our hands were taken from his head and he now not only held all the keys and authorities and powers, but was set apart as the President of the Church, we seemed to feel almost an immediate growth. Although he was a very old man, very aged as judged by the world, he seemed to freshen and liven and throw off much of his years. His sermons were an inspiration. His sweet spirit was everywhere manifest. He was impressive to visitor and member alike.
"Then more recently, the day after his funeral, in July 1972, there came to the Presidency of the Church, President Harold B. Lee, tried and true, educated in the program, spiritual, and above all, called of the Lord. The mantle changed its residence again. It fell on the newly ordained and set apart prophet and president, Harold B. Lee. We have seen this man, already trained and spiritual, grow and magnify his calling. As we see him make pronouncements and decisions, we recognize in them all the voice of the shepherd, the leader of men, a prophet of the Lord, the mantle bearer. (Quoted in The Teachings of Spencer W. Kimball, p. 467.)