Ok here is the long version from a website where people have WAY too much time on their hands:
The ending of The Lord of the Rings can be very confusing. However, a great, and very meaningful elucidation is available from other writings by Tolkien. This entry will seek to bring these to light for those who are not familiar with them and to analyze much deeper what lies in store for those who have come to the Grey Havens, including the Three Hobbits, especially Frodo.
The Grey Havens is one of the last major settlements of the Elves in Middle-earth, found along the Western Coast on the Gulf of Lune. The master of the Havens is Cirdan the Shipwright, a character who has been the chief of the Havens since before the First Age, though, these Havens were in Beleriand at the Falas. He has been charged with the control of the Elves’ departure from Middle-earth. He was also the first inhabitant of Middle-earth to meet the Istari, the Wizards, and he knew that they had come from the Lords of the West. To Gandalf Círdan gave the Ring of Fire, Narya, upon Gandalf’s arrival.
The story of the Elves’ departure from Middle-earth is a key part of the Third Age. They were leaving along the straight path to Tol Eressea, the Lonely Isle along the coast of Aman in the Undying West. The Elves were destined from the start to leave for Aman and Eressea, so that Men could gain dominion in Middle-earth. It is thus as part of this departure that Elrond, Galadriel, and other prominent Elves left upon the great ship with Frodo, Bilbo, and Gandalf. We learn of the Undying Lands in the Silmarillion. They are the lands of the Valar(for those that do not know, they are sort of a replacement of the mythological gods, though they serve a monotheistic God Eru). Picture the Undying Lands as a sort of paradise, inhabited by immortal beings and the land itself, the plants and animals, are equally longeval, which is why the Elves desire to come there. In mortal Middle-earth, they seem to fade and wither, as time passes faster than in the Undying Lands. (Immortal might be a bit too strong of word for the Elves, as they can die, but they are bound within the world until it ends as part of their nature).
To learn more about the importance of the Elves’ departure, please visit the entry Departing Elves. The Departure of Galadriel and Elrond is also connected with the Rings of Power, as the Three Rings lost their powers with the Downfall of the One Ring.
Gandalf’s place on this ship lies in another story. For Gandalf was an Istar, and thus truly a Maia, who had been sent from the West by the Valar to aid Middle-earth in the wars against Sauron. Having achieved this at last, it is only natural for him to return to Valinor in the West, as he does upon the ship of the Ringbearers (he too was one of the bearers of the Elven Rings, and of course was friend of Bilbo and Frodo whom he accompanied). And interesting note is that in Letter 268, Tolkien writes to a fan that the fate of Shadowfax lies in the West as well, for Gandalf naturally would have brought his beloved horse along with him, and given his importance and power, and his being a servant of the Valar, his wishes would not likely be hindered.
This leaves the Three Hobbits who had taken the ship into the West from the Grey Havens. The Lord of the Rings ends with Bilbo and Frodo on the Ship at the Grey Havens, but with not much of a hint as to what lies in wait for them. Sam’s passage over the Sea is marked in Appendix B’s Tale of Years for the Fourth Age.
We can, however, see some of the reason for the Hobbits’ (again, especially Frodo’s) passage into the West from the text of Return of the King, so this is where we will start. The basic idea is that in the Blessed Realm, they can be healed of the poisoning dealt upon them by bearing the immensely One Ring. This is explained very significantly in the last part of the book as it concerns Frodo. It is Arwen who first suggest Frodo’s departure from Middle-earth: “but in my stead you shall go, Ring-bearer, when the time comes, and if you then desire it. If your hurts grieve you still and the memory of you burden is heavy, then you may pass into the West, until all your wounds and weariness are healed” (“Many Partings”). She has realized that there is no permanent healing for Frodo in Middle-earth. Gandalf echoes this later: “Alas! There are some wounds that cannot be wholly cured” (“Homeward Bound”).
Frodo himself sees this as well. He responds to Gandalf saying, “I fear it may be so with mine. There is no real going back. Though I may come to the Shire, it will not seem the same, for I shall not be the same. I am wounded with knife, sting, and tooth, and a long burden. Where shall I find rest?” Gandalf does not answer, but the answer is hopefully on the other side of the Sea. The Shire is in the end saved, “but not for [Frodo].” The process of continual pain continues after the return to Beg End. Frodo states, “I am wounded, wounded; it will never really heal” (“The Grey Havens”). These words are uttered exactly two years after Frodo was wounded by the Morgul-blade at Weathertop. But it is more than just this wound that is poisoning his body, but also the loss of the One Ring. “It is gone forever, and now all is dark and empty.” He did, in the end, not give up the Ring willingly, and because of this, even after its destruction, he is haunted bitterly, and he is moved by a sense of guilt of his failure to give up the Ring.
Thus, we can see that beyond the Grey Havens, Frodo can find healing, as can Bilbo and Sam, though they have not the burdens and ills of Frodo. But what exactly does this passage to the West mean?
. To begin with, the Blessed Realm is Unstained by the Evil of the Dark Lords (Sauron and his predecessor Melkor. And it is a beautiful realm. Thus, we can see the possibility of the land simply allowing the physical and spiritual sickness of Frodo to be healed. He will not live forever though, as the Undying Lands are named only for the Undying beings that typically inhabit the Lands. In several of his Letters, Tolkien makes this clear of the passage of the Ringbearers and Gimli into the West: “they can and will ‘die’ – of free will, and leave the world” (Letter 154 emphasis added). Death by free will is a mark of noble mortals in Tolkien’s created world, a sign of acceptance of one’s fate, which cannot be altered (the conflict between death and immortality is a chief theme in the mythos). From here, we really must look beyond the text for further elucidation of the situation. Tolkien’s letters bring to light very important aspects of the passage into the West for Frodo. In Letter 256, Tolkien explains much of the situation. He begins by discussing Frodo’s “failure” at Mt. Doom to cast the Ring into the fire:
“I do not think that Frodo’’s was a moral failure. At the last moment the pressure of the Ring would reach its maximum – impossible, I should have said, for anyone to resist, certainly after long possession, months of increasing torment, and when starved and exhausted.”
Frodo had done everything that he could to bring about the destruction of the Ring, and because of his effort, his humility and his mercy towards Gollum, “his failure was redressed.” This was recognized by those around him, but Frodo himself, felt differently about the situation. Here, Tolkien begins to describe the passage from the Grey Havens into the West. The idea began with Arwen, he states, though it was made possible through Galadriel and ultimately Gandalf, who was, afterall, an emissary of the Valar, Lords of the West, and friend of Cirdan the Ship-wright.
Tolkien notes in this letter, something already clear in the text, that Frodo, in his darkness, does not feel only physical remnants of pain, “but also unreasoning self-reproach: he saw himself and all that he had done as a broken failure.” He knows that returning to the Shire, as stated in Return of the King, “it will not seem the same, for [he] shall not be the same.” In the end, he had given into the temptation of the Ring (though unavoidably) and desired power and glory, all that the Ring offered, not just a humble “instrument of good.” And, as seen his quote in the text, Frodo still had a desire for the Ring after its destruction.
Gandalf was correct, Tolkien comments, that Frodo could not be cured – “not in Middle-earth.” Thus:
”Frodo was sent or allowed to pass over Sea to heal him – if that could be done, before he died. He would have eventually to ‘pass away’: no mortal could, or can, abide for ever on earth, or within Time. So he went to a purgatory and to a reward, for a while: a period of reflection and peace and gaining of a truer understanding of his position in littleness and in greatness, spent still in Time amid the natural beauty of ‘Arda Unmarred,’ the Earth unspoiled by evil.”
I think the key phrase here is “a period of reflection and peace and gaining of a truer understanding of his position in littleness and in greatness.” The term purgatory does not seem to apply to acceptance of sins and wrongdoings, as in a typical religious usage: Tolkien later, in Letter 325 writes that “the sojourn was a ‘purgatory,’ but one of peace and healing.” The purgatory aspect comes in the form of Frodo’s realization that he is not a failure—realizing the truth about his success, and his humility, rather than his sins.