Jesus Christ is the Light of the world. He said, As long as I am in the world, I am the light of the world (Jn 9:5). Yet, the world rejected this light, this is the condemnation, that light is come into the world, and men loved darkness rather than light, because their deeds were evil (Jn 3:19). From these scriptures we can infer a beautiful symbolism in the signs given by Samuel the Lamanite. At the birth of Christ, when the Light was given to the world, the sign was a light that lasted for 36 hours. At his death, that great light was taken from the world. Accordingly, the sign of his death is the withdrawal of light, even for three days.
That the darkness lasted for three days is also symbolic of the time between the Savior's death and Resurrection. In the Old World, the sign of his death was the same, except for the interval, for the darkness only lasted for three hours (Lu 23:44-45).
Bruce R. McConkie
"While our Lord's body lay in the tomb, while his eternal Spirit preached among the righteous dead, darkness enshrouded the Americas. Far removed though they were from the criminal events, no Nephite and no Lamanite would be unaware that their prophets had foretold the death of their Messiah and said that it would be known by three days of dooming darkness. Where else in all the history of the earth have continents been enveloped in darkness for three days? How could such an event do aught but witness the truth of the promised event?" (The Promised Messiah, p. 540)
Joseph Fielding Smith
"Surely no one who believes in the scriptures and is acquainted with the great and varied miracles performed by Jesus when on the earth, can consistently feel that he could give eyesight to the blind, cleanse lepers, command the storms to cease, and raise the dead, and would be unable to control the light and the darkness on any part of the earth. It would be just as easy for him to cause darkness on one hemisphere for three days as it would on the other for three hours." (Answers to Gospel Questions, vol. 3, p. 45)