I have written often about the "keys of the Priesthood". I think these explanations about the meaning of that term are very good:
President Joseph F. Smith: “The Priesthood in general is the authority given to man to act for God. Every man that has been ordained to any degree of the Priesthood, has this authority dedicated to him.
“But it is necessary that every act performed under this authority, shall be done at the proper time and place, in the proper way, and after the proper order. The power of directing these labors constitute the keys of the Priesthood. In their fullness, these keys are held by only one person at a time, the prophet and president of The Church. He may delegate any portion of this power to another, in which case that person holds the keys of that particular labor. Thus, the president of a temple, the president of a stake, the bishop of a ward, the president of a mission, the president of a quorum, each holds the keys of the labors performed in that particular body or locality. His Priesthood is not increased by this special appointment, for a seventy who presides over a mission has no more Priesthood than a seventy who labors under his direction; and the president of an elders’ quorum, for example, has no more Priesthood than any member of that quorum. But he holds the power of directing the official labors performed in the mission or the quorum, or in other words, the keys of that division of that work. So it is throughout all the ramifications of the Priesthood—a distinction must be carefully made between the general authority, and the directing of the labors performed by that authority.” (“Distinction between Keys of the Priesthood and Priesthood,” Improvement Era, Jan. 1901, p. 230.)
President Joseph Fielding Smith:
“These keys are the right of presidency; they are the power and authority to govern and direct all of the Lord’s affairs on earth. Those who hold them have power to govern and control the manner in which all others may serve in the priesthood. All of us may hold the priesthood, but we can only use it as authorized and directed so to do by those who hold the keys.
“This priesthood and these keys were conferred upon Joseph Smith and Oliver Cowdery by Peter, James, and John, and by Moses and Elijah and others of the ancient prophets. They have been given to each man who has been set apart as a member of the Council of the Twelve. But since they are the right of presidency, they can only be exercised in full by the senior apostle of God on earth, who is the president of the Church.
“May I now say—very plainly and very emphatically—that we have the holy priesthood and that the keys of the kingdom of God are here. They are found only in The Church of Jesus Christ of Latter-day Saints.
“By revelation to Joseph Smith, the Lord said that these keys ‘belong always unto the Presidency of the High Priesthood’ ( D&C 81:2 ). . . .
“Now, brethren, I think there is one thing which we should have exceedingly clear in our minds. Neither the President of the Church, nor the First Presidency, nor the united voice of the First Presidency and the Twelve will ever lead the Saints astray or send forth counsel to the world that is contrary to the mind and will of the Lord.
“An individual may fall by the wayside, or have views, or give counsel which falls short of what the Lord intends. But the voice of the First Presidency and the united voice of those others who hold with them the keys of the kingdom shall always guide the Saints and the world in those paths where the Lord wants them to be. . . .
“I testify that if we shall look to the First Presidency and follow their counsel and direction, no power on earth can stay or change our course as a church, and as individuals we shall gain peace in this life and be inheritors of eternal glory in the world to come.” (In Conference Report, Apr. 1972, pp. 98–99; or Ensign, July 1972, pp. 87–88 .)