What is the LDS Law of Common Consent and why is it important? The LDS Church is perhaps unique in the idea that instruction and change within the Church isn't simply automatic &mdash; that Church leaders can't simply do what they want.  This doctrine is embodied in the LDS Church's Law of Common Consent.

What is the Law of Common Consent, including scriptural basis and official Church teachings, and why is it important?
[The Law of Common Consent] is that in God’s earthly kingdom, the King counsels what should be done, but then he allows his subjects to accept or reject his proposals. Unless the principle of free agency is operated in righteousness men do not progress to ultimate salvation in the heavenly kingdom hereafter. Accordingly, church officers are selected by the spirit of revelation in those appointed to choose them, but before the officers may serve in their positions, they must receive a formal sustaining vote of the people over whom they are to preside.1


Scriptural Basis:


Doctrine &amp; Covenants 20:65-those ordained need the vote of the church
Doctrine &amp; Covenants 26:2-probable first use of 'common consent'
Exodus 24:3-people agree to do what Moses tells them is from God
Numbers 27:19-Joshua placed before the priest and congregation
Acts 15:25-chosen men sent with Paul and Barnabas
Mosiah 29:26- Now it is not common that the voice of the people desireth anything contrary to that which is right
Alma 29:4-God grant unto us our desires, good or evil


Elder Loren C. Dunn explained the responsibilities that accompany the sustaining process (this answers why it is important):


  When we sustain officers, we are given the opportunity of sustaining those whom the Lord has already called by revelation. … The Lord, then, gives us the opportunity to sustain the action of a divine calling and in effect express ourselves if for any reason we may feel otherwise. To sustain is to make the action binding on ourselves to support those people whom we have sustained. When a person goes through the sacred act of raising his arm to the square, he should remember, with soberness, that which he has done and commence to act in harmony with his sustaining vote both in public and in private


Another good article on this subject is The Law of Common Consent, by Matthew O. Richardson. While it may not be official LDS doctrine it is well written with several citations to scriptures, prophets, and history of this practice.

1 https://www.lds.org/manual/doctrine-and-covenants-student-manual/section-26-the-law-of-common-consent?lang=eng