[Mithalwen]

I am sure you will get more erudite answers with references, but this is an attempt at a "basic" answer since I am not at home.

There are two main aspects to this. One is cultural the other is to do with the physical nature of the elves.

When the Elves first awoke at the dawn of time, some went to the West to live with the Valar (angelic guardians of the world) and others remained in Middle Earth. Galadriel is one of the few reamining exiles in Middle Earth. She was born in the West but after a revolt against the Valar she came to Middle Earth. The Exiles, had learnt much from the Valar and as a result were much more powerful, cultured and sophisticated than the elves who remained The exiles return was teh catalyst for so much bloodshed and war that many of the silvan elves (the ones who had never left middle Earth) rejected the "culture" of the Exiles (and the Valar) and deliberately led a simple life, "keeping themselves to themselves". Think of the difference between Galadriel, Glorfindel and even Gildor who know what is going on and Haldir or even Legolas, who has travelled much less and often knows less than Aragorn although he is so much older.... Galadriel is an exile but her people are Silvan. She is the most powerful elf remaining in Middle Earth. Part of her power is bound in the ring and will be lost with it. If she goes into the west her relative status will also be lower - instead of being a queen she will be subject again to the Vala (this is a simplification but the full gory details are in the Silmarillion- which I am assuming you haven't yet read).

The other part of the answer is that even if she stays, she will not be able to hold back time. The lives of elves are linked to the existance of the world (Arda). As long as the world lasts they are not truly deathless, and if they are slain they may take up physical bodies again. Whereas the spirits of men are released from the confines of the world when they die. However although they do not die they do change. If they remained in Middle Earth, the spirits of the elves would eventually "burn" out their bodies and they would become spirit beings only.
At the time of LOTR the elves are weary of the world. Their endless lives are a burden - the world both changes but also stays the same - for them there is nothing new. They are a people in decline. Either they will leave or they will stay and withdraw to the simple, primitive life and less and less contact with the increasingly dominant race of men and eventually fade away.

This makes sense if you know that Tolkien was trying to create a "Mythology" for England. Elves are immortal - but they are also clearly not any more in evidence in England. Most of the legends and stories we have of elves, fairies, pixies etc are of tiny, flimsy folk, far emoved from the elves of LOTR. To 'fit' the elves must have departed or diminished. First in culture, and presence, and then when they became beings of spirit, their presence might be sensed but their true nature forgotten resulting in the diminished size of the elves of English folklore.

I feel I have made a bad job of this, but I hope some of it may be of use.