The earth will be transformed on two separate occasions. At the beginning of the Millenium, the earth will be transformed from a telestial state to a terrestial one. This will be similar to the paradise of the Garden of Eden before the fall of Adam. The second transformation of the earth will occur at the end the little season (after the Millenium) when the earth will be transformed into a celestial sphere for those worthy of a celestial glory. Joseph Fielding Smith explains how this passage from Isaiah is referring to the first of these two earthly transformations.
Joseph Fielding Smith
"This earth is filling the measure of its creation. (Sec. 88:18-26.) Today it is passing through its mortal state. The time will come when it shall die and pass away as do all things upon it. Isaiah says: ’The earth mourneth and fadeth away, the world languisheth and fadeth away, the haughty people of the earth do languish.’(Isa 24:4)
“’The earth is utterly broken down, the earth is clean dissolved, the earth is moved exceedingly. The earth shall reel to and fro like a drunkard, and shall be removed like a cottage; and the transgression thereof shall be heavy upon it; and it shall fall, and not rise again.’ (Isa 24: 19-20) Again he declares: ’Lift up your eyes to the heavens and look upon the earth beneath; for the heavens (i.e. the heavens surrounding the earth) shall vanish away like smoke, and the earth shall wax old like a garment, and they that dwell, therein shall die in like manner.’ (Isa 51:6.) Here we have predictions that the earth shall pass away, die, and all its inhabitants shall also die in like manner. This truth was not generally and correctly understood until the Lord made known in revelations to Joseph Smith that this should be the case. When Isaiah said the earth should ’fall and not rise again,’ the interpretation is that it should not be restored to the same mortal or temporal condition. When the earth passes away and is dissolved it will pass through a similar condition which the human body does in death….The ‘new heavens and new earth’ referred to in this scripture [Isa 65:17], and also in Section 101:23-31, had reference to the change which shall come to the earth and all upon it, at the beginning of the Millennial reign, as we declare in the tenth article of the Articles of Faith. This is the renewed earth when it shall receive its paradisiacal glory, or be restored as it was before the fall of man. (See Compendium, art, ”Millennial Reign,“ p. 202.) ‘The new heaven and new earth’ we are discussing in Section 29, is the final change, or resurrection, of the earth, after the ‘little season’ which shall follow the Millennium.” (Church History and Modern Revelation, vol. 1, p. 132)