Priesthood Purpose

The Lord:
 34 Behold, there are many called, but few are chosen. And why are they not chosen?
 35 Because their hearts are set so much upon the things of this world, and aspire to the honors of men, that they do not learn this one lesson—
 36 That the rights of the priesthood are inseparably connected with the powers of heaven, and that the powers of heaven cannot be controlled nor handled only upon the principles of righteousness.
 37 That they may be conferred upon us, it is true; but when we undertake to cover our sins, or to gratify our pride, our vain ambition, or to exercise control or dominion or compulsion upon the souls of the children of men, in any degree of unrighteousness, behold, the heavens withdraw themselves; the Spirit of the Lord is grieved; and when it is withdrawn, Amen to the priesthood or the authority of that man.
 38 Behold, ere he is aware, he is left unto himself, to kick against the pricks, to persecute the saints, and to fight against God.
 39 We have learned by sad experience that it is the nature and disposition of almost all men, as soon as they get a little authority, as they suppose, they will immediately begin to exercise unrighteous dominion.
 40 Hence many are called, but few are chosen.
 41 No power or influence can or ought to be maintained by virtue of the priesthood, only by persuasion, by long-suffering, by gentleness and meekness, and by love unfeigned;
 42 By kindness, and pure knowledge, which shall greatly enlarge the soul without hypocrisy, and without guile—
 43 Reproving betimes with sharpness, when moved upon by the Holy Ghost; and then showing forth afterwards an increase of love toward him whom thou hast reproved, lest he esteem thee to be his enemy; (D&C 121)

Joseph Smith:
John Taylor, the third President of the Church, reported: “Some years ago, in Nauvoo, a gentleman in my hearing, a member of the Legislature, asked Joseph Smith how it was that he was enabled to govern so many people, and to preserve such perfect order; remarking at the same time that it was impossible for them to do it anywhere else. Mr. Smith remarked that it was very easy to do that. ‘How?’ responded the gentleman; ‘to us it is very difficult.’ Mr. Smith replied, ‘I teach them correct principles, and they govern themselves.’" (John Taylor, “The Organization of the Church,” Millennial Star, Nov. 15, 1851, p. 339)

The Modern Church (From Handbook 2):
2.1.1 Priesthood Keys Priesthood keys are the authority God has given to priesthood leaders to direct, control, and govern the use of His priesthood on earth. The exercise of priesthood authority is governed by those who hold its keys (see D&C 65:2; 81:2; 124:123). Those who hold priesthood keys have the right to preside over and direct the Church within a jurisdiction.