In the Church of Jesus Christ of Latter-day Saints before anyone, including the President of the Church himself, can preside and govern in their office, they must first be sustained by the common consent of the members of the Church.
The way this is done is that when a person is called to a position in the church their name is presented to the congregation during the regularly held meetings where the person conducting says, "It is proposed that (name of the person) be sustained for (name of the position). Those in favor my manifest it by the uplifted right hand." After this has been done, the congregation is next instructed, "Those who oppose, if any, may manifest it." In this way the members of the LDS church show by their common consent whether or not they sustain that particular person to serve in that particular position.
To some, this may seem that the Church operates as a democracy, where matters are decided upon by a majority vote but that's not the case. The sustaining of people to various positions in the Church is not a vote to elect or even to nominate someone to anything. Instead, it is a time when each LDS member affirms their faith and commitment to Jesus Christ.
To understand why this is the case we must first understand that the LDS Church is a theocracy, meaning that it is a government run and operated by God, Himself. Members of the LDS Church don't believe that Christ is the head of their church just because they follow his teachings. Instead, they believe that He is literally and personally directing the affairs of the church, giving it continual instructions and guiding its operation.
He does this by revealing to those in authority which person He wants to serve in which position. Therefore, when a person's name is read before the congregation for their sustaining vote, they are not voting on whether the person should or should not be given the position and neither are they being nominated to fill a position.
What is being asked of the members is whether or not they will accept the person Christ has chosen to fulfill a certain position in His church. That is why, when members of the LDS Church raise their hand in support of a person being called, they are really affirming their commitment to Christ and their allegiance to His rule over them.
The first true theocracy we know of began when the Israelites were brought out of Egyptian bondage because it was the Lord who was in charge of and directed their exodus. It was He who called Moses to go unto Pharaoh and it was God who told Moses what to say. As such, Moses was simply acting under orders. The exodus was not his idea nor was his journey into the wilderness and even their entry into the promised land. Each of those decisions were determined by God. At every step of the way, Moses was doing only that which God had instructed him.
As Moses got old it was God who told Moses that Joshua was to be his successor and when the Israelites entered the promised land it was God who told Joshua what action to take and what to say to his people. After the Israelites had settled into the area and Joshua died, God continued to give direction to His people through the medium of judges and prophets. As such, God continued to be directly in charge of ruling over His people in the same way that a king rules over his people. And, just as a king resides in one place yet is able to govern his entire kingdom through the use of appointed messengers, God likewise governs mortal men from heaven through the use of appointed messengers who convey His decrees to His people.
One such messenger was a prophet named Samuel. In his day, it was through Samuel that the Lord gave direction to His people and it was through Samuel that the people received answers from God about their concerns. This is why their form of government was a true theocracy.
But as Samuel got old, his two sons, Joel and Abiah, were made judges in the land but they walked not in the ways of God. Instead, they "took bribes and perverted judgment. Then all the elders of Israel gathered themselves together, and came to Samuel unto Ramah, And said unto him, Behold, thou art old, and thy sons walk not in thy ways: now make us a king to judge us like all the nations. But the thing displeased Samuel, when they said, Give us a king to judge us. And Samuel prayed unto the LORD. And the Lord said unto Samuel, Hearken unto the voice of the people in all that they say unto thee: for they have not rejected thee, but they have rejected me, that I should not reign over them." (1 Samuel 8:1-7)
When the people presented their request to Samuel, he felt bad because it was the behavior of his two sons that had precipitated this request and, as we look at the complaint of the people, it's understandable why they didn't want to be governed by two corrupt judges. However, that's not how God saw it. He had appointed these judges and they were under His direct control. If they did not perform their duties according to God's satisfaction He would deal with them accordingly.
When the Israelites asked Samuel to have God "make us a king to judge us like all the [other] nations" Samuel was put in the position of asking the heavenly King to let someone else take His place. This is why God responded by saying, "they have not rejected thee but they have rejected me that I should not reign over them."
What the people of Israel should have done was complain to God about Joel and Abiah, then relied on Him to fix the problem. Instead, they decided to correct it themselves rather than trusting in God. In effect, they wanted to fire God's appointed judges themselves and then implement their own solution.
The Church of Jesus Christ of Latter-day Saints operates as a theocracy in the same way the government of Israel operated during the reign of the judges. It is Jesus Christ who is the personal head of the Church. As such, it is He who dictates the rules and determines who His messengers will be. If they do not perform their duties to His satisfaction, then it is His responsibility to take care of them, not ours.
This is why, when members of the LDS Church raise their hand to sustain someone, they are affirming their faith in Christ by acknowledging His rule over them, and showing their willingness to submit themselves to His authority. The raising of the hand isn't about approving or disapproving the selection of the person being called. It's about us signifying our approval or disapproval of God's decision.
However, members of the LDS Church do not vote on the rules or beliefs of the Church. They only raise their hand to sustain or not sustain the person being called to serve. The reason is that once a person has been sustained we are implicitly agreeing to accept their decisions. For example, when we raise our hand to sustain the President of the Church we are agreeing to submit ourselves to his authority which includes obeying the rules, commandments, counsel, and advice he gives. And the same applies to the members of the Quorum of the Twelve, the General Authorities, Stake Presidents, and Bishops.
But once we have sustained someone, that is not the end of it. Each year we are again asked to sustain all those who are currently serving. In fact, we are asked to sustain many of them three different times each year. We sustain all the current General Authorities of the Church during the first General Conference of each year. We are then given the chance to sustain the same people during the first Stake Conference of each stake every year and we are again asked to sustain the same people during the annual Ward Conferences of each ward.
The natural question this raises is: If we have already given our sustaining vote the first time these people were presented to us, then why do we need to continue repeatedly sustaining them? And why do we even sustain anyone at all if the purpose of it is to show God our commitment to Him? After all, we already made that commitment when we agreed to be baptized.
There are two answers to this question. The first is that giving our sustaining vote doesn't just show our commitment to God but it also shows our commitment to the person being presented to us. The word "sustain" means "to uphold, support, help, encourage, prop up, buttress, assist, defend, buoy up and care for." When we raise our hand to sustain someone we are not just giving our permission for them to hold a certain position but are pledging our support to help them succeed in that position and to make their duties easier for them to bear. It doesn't mean that we tell them how to do their job or what decisions they should make but it does mean that we are willing to carry out any assignment or follow any instruction, request, or directive they may give us.
When we fulfill the commitment we make when sustaining someone we are also reaffirming the commitment we made to God to help build up His kingdom and show that we are willing to faithfully serve Him. Since God is the one who calls each person, and every position in the Church is important, then when we help support someone in their calling we are helping them do their part in strengthening and building Christ's kingdom here on earth. Since none of us are perfect and each of us has faults, weaknesses, and shortcomings, when we sustain people in their callings we are also helping them become better Saints of God, which, in turn, helps God perfect His children. This is one way our sustaining vote affirms our commitment to God.
The second way has to do with how God governs.
When the Israelites came to Samuel asking for a king, God could have chastised them for their lack of faith in Him but, instead, He told Samuel, "Hearken unto the voice of the people." Why did He say that, especially given the fact that He, as the King, could legally impose His will on them? Imagine an earthly king, whose people say they don't like the way he is governing them, telling his governors to listen to what the people are saying! No king runs their kingdom that way yet that's the way God governs His kingdom.
In earthly kingdoms, kings rule over the people within their sphere of power whether those people accept him or not. If someone doesn't want to be ruled over by their king, it doesn't matter. He is their king anyway and they either do as he says or be punished. A new child born into a kingdom is automatically under the king's rule even though they never asked to be subservient to him. But that's not how God treats His subjects.
God only wants those in His kingdom who want to serve Him. Those who don't want to serve are free to go somewhere else because He will not force anyone to be subservient to Him. Therefore the only people who can belong to the kingdom of God are those who willingly, voluntarily, and deliberately choose to accept Him as their king. Although baptism is the gateway into Christ's kingdom, every person has to make a daily personal choice whether they want to be an active part of Christ's church or not.
The Lord explained that those who have been baptized into the Church but "who are not valiant in the testimony of Jesus [will] not obtain the crown over the kingdom of our God" (D&C 76:79). To be valiant means to serve God faithfully. Only those who serve God with all of their heart, mind, and soul are worthy to inherit eternal life but such an attitude can only happen by choice. Those who do not want to serve God fully and faithfully are not entitled to the benefits of His kingdom, in which case there are other kingdoms they can belong to.
While in this world our citizenship in the kingdom of God is under probation and, as such, we are given ample opportunities to choose either way. Some people begin their membership in the Church with a great desire to serve, only to change their mind and choose to become inactive or less active. Yet, in time, they may choose to change their mind again and decide to become a valiant member.
Because our attitudes are susceptible to change we are asked to declare our feelings about God each year. And if there ever came a time when the common consent of God's people didn't sustain the person God chose to govern them, especially the President of the Church, then the church will have rejected God. That wouldn't change who God is but it would change our relationship to Him. Like Israel, we would choose to be governed by someone other than God. Therefore, when we raise our hand to sustain someone we are expressing our commitment to God, Himself. It is our declaration of allegiance to Him and our willingness to obey Him.
But the LDS Church is not the only one who claims that Christ is the head of their church. Many other Christian faiths make the same claim and many of them choose their leaders by common consent, however, their organization is not a theocracy but a democracy. The reason why is because, when a position becomes available in most churches people campaign for it. Resumes are submitted, education is highlighted, experiences are touted, and credentials are dislayed. The person applying for the position seeks to impress the people doing the hiring to select them and, once hired, in many cases, if the church is not satisfied with their performance they are removed by the common consent of the congregation.
By comparison, in the LDS Church the person in authority over a certain position seeks for and receives revelation from God as to whom God wants to fill that position. There is no consideration of resumes, education, or experience. The only credentials needed are those of faithful service in Christ's church.
In most churches all a person has to do in order to serve in a position is to garner 51% of the vote but if they had to have 100% of the vote, hardly anyone would ever be chosen to fill any position. Yet, when people are called to serve in the LDS Church, a sustaining vote of 100% happens routinely and consistently.
Because people hold a wide variety of views and feelings, in most churches where common consent is used to conduct business there is much discussion and often much arguing before a vote is taken. However, in the LDS Church there is no debate. The only thing that is being asked is whether the members will accept or reject the person being presented. It is a straight yes or no vote.
But when members of the LDS Church raise their hand to sustain a person they are doing more than simply giving their permission for that person to serve. They are declaring their commitment both to the person being called and to God. Although most LDS members already are devoted to Christ and His kingdom many may not fully appreciate the gravity of what they are doing when they raise their hand to give their common consent.