In the movies, all the Elves are pretty much packing their Elfy bags and shuffling off to somewhere, why were they leaving and where were they all going to?
It’s explained much better in the books, partly LotR and partly The Silmarillion: There’s a lost land to the West where the demigods (Valar) live. Ages ago, many elves lived there having been summoned from Middle-Earth where they were born. Some returned to Middle-Earth as part of an effort to recover the epic gemstones known as Silmarils, and were exiled because at one point this involved going to war unjustly against their fellow Elves. Later, the Valar took pity and, after dealing with the bad guy who stole the Silmarils in the first place, revoked the Ban. Since then those exiled Elves have been gradually drifting back to the western lands (now placed beyond the world so that only Elves can go there). There is also a general invitation to any other Elves (for there are several races of them, not all of whom ever went into the West in the first place) to go should they feel like it; that would cover Legolas and his people. Galadriel, on the other hand, was one of the “rebels” described above.
Malacandra hits all the major notes, but misses one important one that you may or may not have picked up on - the boat that Frodo boards at the end of the movies (and the books) is headed to the West as well. After all his suffering, it is the only place he can go to find peace, and he, in return for his services as ring bearer, is granted the exception allowing him to go.
It’s complicated – kind of.
The idea is that Middle Earth was shaped by angelic beings Ainur (Valar and Maiar) – sub creators to what Tolkien would’ve called God. God introduced into the shaped world his children, elves and men. These children both posses a spirit but have different natures. The elves last until the unmaking of the world; if their bodies die they are reclothed in new ones. Men die and pass outside the world and escape the long ages.
Elves came first and given their nature were brought by the Ainur to live with them in a land to the west. Ultimately evil (a fallen Valar called Melkor) corrupts the bond between one of the elven “tribes” and the Valar leading to a rebellion and ultimately exile in Middle Earth.
After 500 years of fighting Melkor, his lieutenant Sauron and their horde of orcs, trolls, balrogs, dragons, werewolves and vampires the elven kingdoms are shattered. But the Valar and other rise up and cast down Melkor and allow the elves to return to the west. However not all are willing to leave. So the invitation stands and is basically extended to elves that never went west in the first place.
Or what Malacandra said.
Again, three movies wasn’t enough for this story.
Legolas also took Gimli with him to Valinor, without any particular permission to do so and for no other reason than their friendship. Sylvan elves, I tell ya. (this doesn’t happen in the movie, to be clear).
I would hope that was apparent to those who hadn’t read the books. I first read them forty years ago, so it wasn’t missed on me.
Was it apparent that Arwen (Liv Tyler) was 2K years old and a distant relative of Aragorn? Probably not.
Is that from LOTR or the Simirilion, however one spells it?
Maybe I skilled the genealogy and kissing parts…
LOTR in the appendices.
I can’t recall that Elros–Elrond’s brother, Arwen’s uncle, Aragorn’s many-greats grandfather–ever gets referenced in the movies.
It’s worth noting that basically any ‘noble’ wife Aragorn, or his predecessors, could have found would have been a closer relative than Arwen, probably with descent from Elendil (and therefore Elros) in multiple lines. Aragorn himself was descended from both of Elendil’s sons, Isildur and Anárion, by documented lines and probably several times over if all the Kings’ and Chieftains’ wives were counted in. There is even a suggestion that Éowyn could be of Anárion’s blood, “slender and tall, with a grace and pride that came to her out of the South [Gondor] from [maternal grandmother] Morwen of Lossarnach.”
Thanks!
I did indeed skip those. 
Many of the appendicies are just lists and geneologies, but The Tale of Aragorn and Arwen, Appendix A, is a lovely little short story in its own right.
It’s mentioned in the appendices as a “We hear that…” note, with the remark that it was unusual - indeed, unheard of - that a Dwarf would want to go into the West for any reason, or that the Valar would allow it; and it might be that Galadrie*l herself obtained permission for this. “More cannot be said of this matter.”
*Galadriel was back in very good odour, for refusing the Ring when Frodo willingly offered it to her.
Nor three books.