Galadriel is describing here the outcome of the destruction of the Ring, obviously, and the result it will have on the works she has created with her own ring. Galadriel was feeling weary in Middle Earth prior to the forging of the rings. Celebrimbor made the Ellessor for her, which had the power to preserve life/slow time etc (everything bloomed green around it), to help her. She gave this to her daughter when Nenya was given to her, the elven ring having similar, but more potent powers.Yet if you succeed, then our power is diminished, and Lothlórien will fade, and the postThreadIDes of Time will sweep it away. We must depart into the West, or dwindle to a rustic folk of dell and cave, slowly to forget and be forgotten.
Galadriel fears once the ring is destroyed, everything made with Narya will diminish. So what exactly did she create with Narya? The elven rings did not grant their wielders great power or amass them great piles of gold. Their effects were far more subtle. I think they helped to heal and stay off the ravages of time.
The popular conception of elves being immortal and not ageing is actually incorrect. They did age, but in a slower and different fashion to Men. Mandos warned in the Doom of the Noldor...
Tolkien explains this fate in more detail in Morgoth's Ring...And those that endure in Middle Earth and come not to Mandos shall grow weary of the world as with a great burden, and shall wane, and become as shadows of regret before the younger race that cometh after.
Also in Morgoth's Ring is a piece where Finrod is talking about death to a wise woman when he first discovered Men back in the First Age. Here he describes...As ages passed the dominance of their fea (spirit) ever increased, "consuming" their bodies. The end of this process is their "fading", as Men have called it; for the body becomes at last, as it were, a mere memory held by the fea; and that end has already been achieved in many regions of Middle Earth.
So, elves do age and their bodies become consumed by the their fea. If this was noticeable by Finrod right back in the First Age, only a few centuries after the Noldor returned to Middle Earth, by the time of the War of the Ring, over 6000 years later, many of the elves still around must be feeling well worn. The surviving conclaves of Elves who had either returned from Valinor, or who like Cirdan and Celeborn were old enough to remember those times, were centered around where the rings had been... The Havens, Rivendell and Lothlorien. I think it was only the rings that were keeping the ravages of time away from these ancient elves. With the passing of the rings they either had to leave Middle Earth or literally fade away.For know, it is not otherwise with the Quendi themselves: their health and stature is diminished. Already those of us who dwell in Middle Earth, and even we who have returned to it, find that the change of their bodies is swifter than in the beginning.
This fading, Finrod accounted to be part of the shadow of Melkor. As the body was made from the material of the earth, and that material had been tainted by Melkor, their bodies were not as durable as Eru had originally intended them to be.