The two foundational aspects of Elven, especially High Elven, life that make them seem magical are (1) artisanship at the limit and (2) immortal preservation. Almost everything about Tolkien's Elves that makes them different from Men comes down to one of these two, or both. We learn late in LOTR, and I think this is the only place it is actually mentioned, that Elves don't sleep and they don't dream. When Aragorn and Gimli settle down for the night, Legolas simply lays back and spends the night remembering ages past. Elven memory is such that they can remember events as if they were really there; that is the closest Elves generally get to dreams, although perhaps it would be better to say that dreams are the closest we get to Elven memory. Elven immortality is not merely a happenstance, but something that follows from their inner principle; everything they are involves the preservation of what was past. This is why the Elves who went to the Blessed Realm are so powerful: they preserve something of the Blessed Realm even into the changeable environment of Middle Earth.
We are told in The Lord of the Rings and elsewhere that at the end of the Third Age there were three major strongholds associated with the High Elves (although there were Elves elsewhere, most notably in Mirkwood): the Grey Havens, Imladris (also called Rivendell), and Lothlorien. Each of these represents a distinct kind of preservation. (In a letter somewhere, Tolkien explicitly points this out with regard to Rivendell and Lorien, so this is at least partly there even at the level of authorial intent.) Círdan, Elrond, and Galadriel have the positions they do in Elven society because they are the master-overseers of the Elven arts that involve these preservations.
The form of preservation that is represented by the Grey Havens and Círdan is escape from what destroys. A long time ago, I used to be puzzled about Círdan. Unlike Galadriel, he never went to the Blessed Realm and never saw the Trees. This is also true of Elrond, who is too young, but Elrond's place is not puzzling because he was the herald of Gil-galad the High King, who was the son of Fingon the High King, who had been to the Blessed Realm; and Elrond is himself the son of Eärendil, who had (and who had essentially saved the world). But not only did Círdan never go to the Blessed Realm, he has no family who had. But there is a reason for that. If you really pay attention to what is said of him in LOTR and The Silmarillion, it becomes clear that he is very, very old, so old, in fact, that it is strongly suggested that he goes back to the Awakening, or perhaps the second generation. And that this is indeed what Tolkien himself thought likely is clear from some of the works Christopher Tolkien has published since. Círdan may be so old he has no father, or at least no grandfather; he's one of the first Elves, perhaps the oldest Elf still alive in all of Middle Earth. He has spent much of that time interacting with Ulmo and Ossë. And over the years he has come to be the one maintaining the connection with the Blessed Realm, a spark of hope and a last way out.
Rivendell and Elrond, however, represent a different kind of preservation: that of memory and lore. In Rivendell Elrond is a master of lore, and his hall is a hall for telling and singing stories. This kind of preservation we know quite well, although here as elsewhere the arts of it are taken to a form greater than Men could possibly achieve.
Lorien and Galadriel represent another kind of preservation. To step into Lorien is like stepping into another world entirely. And that's the point. Lorien is not entirely this world. The Elves may have the ability to remember events as if they were really there, but Galadriel has outdone them all: she has remembered things so vividly that the world around her takes on something of their form. Lorien is Galdriel's memory of the Blessed Realm to the extent that changeable Middle Earth can bear it. She tells us this herself:
I sang of leaves, of leaves of gold, and leaves of gold there grew:
Of wind I sang, a wind there came, and in the branches blew.
While in Imladris life is preserved as memory, in Lorien memory is preserved as life. Memory flows through Imladris like water; in Lorien it is like the air you breathe.
These, then, are the three kinds of preservation, escape, memory, and life, and in the last strongholds of the Elves we find them each taken to their ultimate extent.
But, of course, in Middle Earth preservation does not suffice, and it does not save. It merely holds things off for a time.