D&C 90

The Lord provided some additional instruction for counselors in presidencies as provided additional instruction to the Prophet on the establishment of the First Presidency. To the Prophet as President he teaches -

"...thou art blessed from henceforth that bear the keys of the kingdom given unto you; which kingdom is coming forth for the last time." (Doctrine and Covenants Section 90:2)

And -

"...through you shall the oracles be given to another, yea, even unto the church." (Doctrine and Covenants Section 90:4)

It was through the President of the First Presidency that truths and revelations were to come to the Church. To the Presidents counselors the said -

"...verily I say unto thy brethren, Sidney Rigdon and Frederick G. Williams, their sins are forgiven them also, and they are accounted as equal with thee in holding the keys of this last kingdom..." (Doctrine and Covenants Section 90:6)

At first it may seem the counselors also hold the keys but this becomes more clear as we read -

"...the keys of the kingdom, which belong always unto the Presidency of the High Priesthood..." (Doctrine and Covenants Section 81:2)

And

"The Presidency of the High Priesthood, after the order of Melchizedek, have a right to officiate in all the offices in the church." (Doctrine and Covenants Section 107:9)

As counselors in presidencies, they hold the full authority to represent the president in his absence in that since the president holds the keys, the collective group of presidency holds the keys. As the president is released the presidency is released and so also the collective authority. Hoyt W. Brewster wrote -

"...While the President obviously presided over all affairs, the counselors in the presidency had authority to act in behalf of the President in his absence or as assigned by him." (Prophets, Priesthood Keys, and Succession, Hoyt W. Brewster )

The presidency , by virtue of their calling -

"That thereby they may be perfected in their ministry for the salvation of Zion, and of the nations of Israel, and of the Gentiles, as many as will believe;
9 That through your administration they may receive the word..." (Doctrine and Covenants Section 90:8 - 9)

"And this shall be your business and mission in all your lives, to preside in council, and set in order all the affairs of this church and kingdom.
17 Be not ashamed, neither confounded; but be admonished in all your high-mindedness and pride, for it bringeth a snare upon your souls.
18 Set in order your houses; keep slothfulness and uncleanness far from you." (Doctrine and Covenants Section 90:16 - 18)