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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.

Citation

“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

More on power.

“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.