In its most literal sense, "sustain" means to hold up from beneath. Sustain comes from the root "to stretch." In Latin, sustain came to mean to hold, keep, maintain, to cause to endure or continue, to hold onto. It also has the sense of holding by the hand and sustenance.
The Oxford English Dictionary defines sustain as supporting the efforts, conduct or cause of; to succor, support or back up; and to give support to a person's conduct, a cause or a course of action. Sustain also means to hold up, bear the weight of and keep from falling by support from below.
Sustain also has the sense of keeping at something, the sense of stretching for the long haul. While the symbolic act of the sustaining raised hand lasts only a moment, it is emblematic of a commitment for the long term.
Almost every Sunday in sacrament meetings, Latter-day Saints raise their hands to sustain fellow ward or branch members who have been called to positions. Latter-day Saints also regularly sustain their ward and stake leaders and the general authorities of the church. The prophet, his counselors and the Quorum of the Twelve are sustained as prophets, seers and revelators.
When we raise our hands in such sustaining settings, particularly with respect to the prophet, we are uplifting or stretching our hands in a wonderful symbol that represents the definition of sustain. Our raised hands symbolize lifting up from below. By so doing, we are promising to uphold and support him.
We are taught in the Doctrine and Covenants that the First Presidency is "upheld (sustained) by the confidence, faith and prayer of the church" (D&C 107:22).
When we sustain the prophet, we are in a small way performing the role played by Aaron and Hur when they held up Moses' hands during the battle against Amalek.
"When Moses held up his hand ... Israel prevailed and when he let down his hand, Amalek prevailed. But Moses' hands were heavy ... and Aaron and Hur (supported) his hands" and Israel prevailed (Exodus 17:11-12).
In the April 1995 general conference, President Gordon B. Hinckley spoke of the importance of sustaining church officers.
"It may appear as a somewhat perfunctory exercise," he said. "But I remind you that it is an act of grave and serious importance...."
President Hinckley then quoted President John Taylor: "We hold up our right hand when voting in token before God that we will sustain those for whom we vote ... for when we lift our hands in this way, it is a token to God that we are sincere. ... If we agree to do a thing and do not do it, we become covenant breakers."