At the end of the Lord of the Rings, Galadriel hops on a boat and sails away into the West. But wasn't she banned after the kerfuffle caused by Uncle Fëanor?
All was forgiven after the War of Wrath and the Noldor were allowed to return. Actually, all the Elves were strongly urged to return, but some chose to stay in Middle-earth. For them, The Straight Path to Valinor was still available to them for when they chose to leave.
This is explained in the final page of "Akallabêth" in The Silmarillion.
By refusing the One Ring when Frodo offers it to her, and accepting that her own powers will fade, Galadriel proved herself worthy to return to the Undying Lands.
This is not outright stated, but suggested strongly by Galadriel's own words at that time:
I have passed the test. I will diminish, and go into the West, and remain Galadriel.
Tolkien says this in his Letter #320:
Galadriel was a penitent: in her youth a leader in the rebellion against the Valar (the angelic guardians). At the end of the First Age she proudly refused forgiveness or permission to return. She was pardoned because of her resistance to the final and overwhelming temptation to take the Ring for herself.
However, note that the history of Galadriel underwent several revisions in Tolkien's writings; in some of them (but not the one the Silmarillion is based on), Galadriel is entirely innocent of the Kinslaying and goes to Middle-Earth independant of Feanor and the rest of the Noldor; in those versions she did not need an explicit pardon, but stayed in Middle-Earth because she loved Lothlorien too much to leave.
The answer appears in Tolkien's The Road Goes Ever On
"The question Sí man i yulma nin enquantuva? and the question at the end of her song (Vol. I, p. 389), What ship would bear me ever back across so wide a Sea?, refer to the special position of Galadriel. She was the last survivor of the princes and queens who had led the revolting Noldor to exile in Middle-earth. After the overthrow of Morgoth at the end of the First Age a ban was set upon her return, and she had replied proudly that she had no wish to do so. She passed over the Mountains of Eredluin with her husband Celeborn (one of the Sindar) and went to Eregion. But it was impossible for one of the High-Elves to overcome the yearning for the Sea, and the longing to pass over it again to the land of their former bliss. She was now burdened with this desire. In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings."
JRRT, The Road Goes Ever On, 1967
So while a lot of posthumously published material exists about Galadriel, this is the explanation that Tolkien himself chose to reveal to readers, published in 1967.
This answer is based on Tolkien more than his fictional characters, but presents the point that in permitting Galadriel to return to the Undying Lands (his fictional construct of Heaven/Paradise) he was sending a message to his readers, a message of forgiveness and redemption.
In the event, after the fall of Sauron, in reward for all that she had done to oppose him, but above all for her rejection of the Ring when it came within her power, the ban was lifted, and she returned over the Sea, as is told at the end of The Lord of the Rings." (The Road Goes Ever On, 1967)
"The Exiles were allowed to return - save for a few chief actors in the rebellion of whom at the time of L.R. only Galadriel remained." (a letter also dated 1967)
Per the citations above, this was Tolkien doing what he said he didn't like doing in his infamous commentary on Allegory versus Applicability. He was either being allegorical, or was very bluntly moralizing as a result of being a life long and devoted Roman Catholic.
Galadriel is presented as a sinner who has shown that she "rejects the lies of Satan." (baptismal promise, Catholic dogma 101). The forgiveness and redemption of Galadriel is a piece of Christian wish fulfillment. Her sin (along with the other rebellious Noldor) of "turning their backs on the Valar" and by extension Eru the One, Illuvitar, is forgiven in a redemptive act by the active rejection of Sauron (Satan/Evil/Liar). Power for its own sake, which the Ring symbolized, was for Tolkien a great evil.
“We have come from God, and inevitably the myths woven by us, though they contain error, will also reflect a splintered fragment of the true light, the eternal truth that is with God. Indeed only by myth-making, only by becoming 'sub-creator' and inventing stories, can Man aspire to the state of perfection that he knew before the Fall. Our myths may be misguided, but they steer however shakily towards the true harbour, while materialistic 'progress' leads only to a yawning abyss and the Iron Crown of the power of evil.” ― J.R.R. Tolkien
“But the only measure that he knows is desire for power and so he judges all hearts. Into his heart the thought will not enter that any will refuse it that having the Ring we may seek to destroy it. If we seek this we shall put him out of reckoning.” ― J.R.R. Tolkien, The Fellowship of the Ring
The Noldor "fell" when they left the undying lands. JRR Tolkien couldn't help himself. Given his outlook on life, his own fantasy was woven into the fantasy conflict resolution of his magnum opus. Forgiveness and Redemption had to come through, in the last, since that was his hope as informed by his lifelong faith.
It wasn't until I understood JRR Tolkien as a lifelong and devout Catholic that I began to see some of the messages he sent in this story, which I've read over a dozen times. He wasn't very subtle.
Her ban was lifted after she refused the ring, before that she was banned by the Valar for her part in the rebellion, but she actually never took part in the kinslaying, it was just her wish for a own realm to rule that she had to overcome in order to return to Valinor.
Pretty much wut Steffi said,
but to elaborate; Galadriel longed for followers and power, through her wisdom and countless years on middle earth gazing into her mirror, which i believe was somehow entwined with either the simarils or trees of valinor..she deduced that the one ring would only destroy, and she would inevitably come to dominion over nothing. But uhhh yea...Galadriel was extraordinary in power and awe...she was actually Sauron's nemesis and in his discord, he failed to see her.
overall, the story is incredibly epic and after reading numerous essays on the material, i have come to realize the 2 most important parts of the book are when Galadriel refuses the ring and when Frodo commands with the one ring that if Gollum..(and i say gollum cause Smeagol loves his master) lay hands on him he will himself be cast into the fire...the latter actually uses the commanding power of the ring with outright burning authority to inconceivably force the ring to destroy itself...and with Galadriel..the sheer power that was present from her outstretched hand with the adamant upon it, against and yet with the one ring is a staggering revelation..as she would have been a far more detrimental force then Sauron himself. She whom was in direct assent from the crafter of the rings as well as the simarils..with such high desire for worshippers. she would not of slain Sauron but used him as a tool and forced him to his knees as with all of Middle Earth untill she had the Will and the might to breach Valinor itself..which btw valinor has 2 Palantir an easy and convenient means to fray the fabric. As of Melkor she would of released him and made him a puppet and then caused the great war that would have been Tolkiens masterpiece....i feel actually with all his rewrites of Galadriel that he was actually prolly distraught at how rushed he was to get the material published as he hadto retcon to his his endgame..which ...i feel would of been Galadriel taking the ring and convalescing with a confrontation with Eru.