"A Kingdom, Which Shall Never Be Destroyed"
Presidents of The Church of Jesus Christ have taught that Daniel’s prophecy of the stone cut out of the mountain is a prophecy of the growth of the Church. Doctrine and Covenants 65:2 agrees that the gospel will roll forth as the stone cut out of the mountain.
“Daniel, Prophecies of,” Jeffrey R. Chadwick, Encyclopedia of Mormonism
According to Wilford Woodruff, the angel Moroni quoted to the Prophet Joseph Smith from Daniel chapter two which features a prophecy of the latter-day restoration of the gospel in Nebuchadnezzar's dream concerning "what shall be in the latter days." Daniel identified the "head of gold" in the dream as a symbol of Nebuchadnezzar's empire, and latter-day prophets have specified that the stone "cut out without hands" represents the latter-day kingdom of God. The remaining symbols have been interpreted as follows: The "breast and arms of silver" represent the Persian realm that superseded Babylon. The "belly and thighs of brass" prefigure the succeeding Hellenistic states. The two "legs of iron" point to the Roman Empire, foreshadowing the division between Rome and Constantinople. The feet of the image, "part of iron and part of clay," symbolize the European kingdoms that grew out of the dissolving Roman Empire, beginning in the fifth century. Those kingdoms merged the culture of Rome with that of northern and eastern European tribes; hence, the symbolic mixing of iron and clay.
"Quiet Slumber: Revelation through Dreams," Ryan C. Jenkins, Religious Educator 12, no. 1 (2011): 73–89.
Daniel’s confidence in inquiring of the Lord must have been preceded by individual moments with the Lord that gave him unflinching assurance. He was also the recipient of a dream detailing events in the last days. In this case we know “he wrote the dream, and told the sum of the matters” (Daniel 7:1).
“The Stone Cut without Hands,” Spencer W. Kimball, April 1976 General Conference
“This is a revelation [Daniel 2] concerning the history of the world, when one world power would supersede another until there would be numerous smaller kingdoms to share the control of the earth.
“And it was in the days of these kings that power would not be given to men, but the God of heaven would set up a kingdom—the kingdom of God upon the earth, which should never be destroyed nor left to other people.”
“The Church of Jesus Christ of Latter-day Saints was restored in 1830 after numerous revelations from the divine source; and this is the kingdom, set up by the God of heaven, that would never be destroyed nor superseded, and the stone cut out of the mountain without hands that would become a great mountain and would fill the whole earth.”
“The Stone Cut Out of the Mountain,” by Gordon B. Hinckley, October 2007 General Conference
“The Church has become one large family scattered across the earth. There are now more than 13 million of us in 176 nations and territories. A marvelous and wonderful thing is coming to pass. The Lord is fulfilling His promise that His gospel shall be as the stone cut out of the mountain without hands which would roll forth and fill the whole earth, as Daniel saw in vision (see Daniel 2:31–45; D&C 65:2). A great miracle is taking place right before our eyes.”
“The Time Shall Come,” L. Whitney Clayton, October 2011 General Conference “Daniel was a Hebrew slave in Babylon. He was given the opportunity to interpret King Nebuchadnezzar’s dream. Daniel asked God to reveal to him the dream and its interpretation, and his prayer was answered. He told Nebuchadnezzar, ‘There is a God in heaven that revealeth secrets, and maketh known to the king Nebuchadnezzar what shall be in the latter days. … The visions of thy head upon thy bed, are these.’ Daniel said the king had seen a frightening image with a head, torso, arms, legs, and feet. A stone was cut out of a mountain without hands and rolled forth, gradually growing in size. That stone collided with the image, breaking it into pieces, ‘and the stone that smote the image became a great mountain, and filled the whole earth.’
Daniel explained that the image represented future political kingdoms and that ‘in the days of [those future] kings shall the God of heaven set up a kingdom, which shall never be destroyed: … but it shall break’ these kingdoms into pieces and consume them. ‘And it shall stand for ever.’”
“The Church of Jesus Christ of Latter-day Saints membership history,” Wikipedia
Charts showing growth rate of the Church compared to growth rate of world population confirm that although Church growth varies from year to year, membership consistently outpaces world population growth.