The original world as built by the Valar was referred to as Arda Unmarred. This world was effectively destroyed by the wars of the Valar and Melkor, and only Valinor still resembled it in part. Arda Unmarred was a symmetrical world with everlasting light.
Arda Marred was the name given to the world as it is: the world after the wars of the Valar and Melkor, and the dispersing of Melkor's Fëa and hröa throughout the world. It is this world from which are formed the Fëa and hröa of the Children of Ilúvatar, and therefore it is at times a cruel and evil world with plagues, extreme colds, heat, and other concepts which do not exist in Arda Unmarred.
Arda Marred also broke the design of Elvish immortality: in Arda Marred Elves slowly fade, until at last they are little more than wraiths. Only in Valinor was this fading delayed, which is one reason all Elves have no choice but to sail to Valinor in the end. One of the special abilities of the Rings of Power was that they could delay the effects of time, and as such were used by Elrond and Galadriel to preserve their realms. After the destruction of the One Ring in the Fourth Age, the Elvish rings' power over time was also lost, so the last of the Eldar had no choice but to leave Middle Earth and sail west for Valinor.
Arda Healed is the prophecy that Arda Marred will be restored: it will be like Arda Unmarred but better, since it will also incorporate all the good things of Arda Marred. Arda Healed will be created after the Dagor Dagorath, when Morgoth will finally be destroyed, and the world broken. Afterwards, a new world will be created and will be known as Arda Healed.
Galadriel's words while parting with Treebeard at Isengard in The Return of the King are "Not in Middle-earth, nor until the lands that lie under the wave are lifted up again. Then in the willow-meads of Tasarinan we may meet in the spring. Farewell!". This might imply that Beleriand will be recovered after the Dagor Dagorath. It is however unknown, since Arda Healed will contain all the good things of Arda Marred, whether Númenor will also be recovered or not.