Galadriel is the Lady of Lothlórien. Her hair is deep gold and she is as tall as her partner, Lord Celeborn. She, like Lord Celeborn, is unimaginably old, but no mark of this age is visible on her face except in "the wells of deep memory" (2.7.17) in her eyes. Galadriel is also Arwen Undómiel's (extremely well-preserved) grandmother: her daughter, Celebrían, bore Lord Elrond's child. She is the Lady of the Galadhrim, the People of the Trees, who live high in the mallorn trees of Lothlórien, the Golden Forest.
When Galadriel sees the Fellowship standing before her, she knows already that Gandalf the Grey "fell into shadow. He remained in Moria and did not escape" (2.7.18). No wonder Galadriel feels so attached to Gandalf: Galadriel mentions that she is the one who first brought together the White Council, of which Gandalf, Radagast, and Saruman are all members. She had wanted Gandalf the Gray to lead the Council, but that position went to Saruman. It's a shame that she was apparently overruled, since things might have been different in Isengard otherwise.
Galadriel also has unusual compassion: she reaches out to Gimli when Celeborn accuses the Dwarves of rousing Durin's Bane, the Balrog, in Moria, saying: "Dark is the water of Kheled-zâram, and cold are the springs of Kibil-nâla, and fair were the many-pillared halls of Khazad-dûm in Elder Days before the fall of mighty kings beneath the stone" (2.7.28). Gimli, struck by this sudden and unexpected sympathy, immediately becomes a huge fan of Galadriel's. (See our "Quotes and Thoughts" section on "Compassion" for further meditation on Galadriel and Gimli.)
Galadriel tells the company that she and Lord Celeborn have cohabited for "years uncounted" (2.7.31), before the fall of Nargothrond or Gondolin (which are in the First Age; we're now in the Third Age of Middle-earth). During that time, they have struggled against "the long defeat" (2.7.31).
Continually (though slowly), they have been losing ground against the Enemy – Sauron, in this Age. So she is personally committed in this Ring quest, and will do her best to see it go well. Galadriel herself, along with her handmaidens, weaves the cloth of the cloaks that the Elves of Lórien give to the Company; one of the Elves tells Frodo: "You are indeed high in favour of the Lady! [...] never before have we clad strangers in the garb of our own people" (2.8.30).
When Galadriel comes to say a last goodbye to the Fellowship, she already looks diminished, "a living vision of that which has already been left far behind by the flowing of Time" (2.8.46). As beautiful as Galadriel is, she is part of Middle-earth's past. As the carriers of the Ring, the Fellowship literally holds the future of Middle-earth in their hands. So in some ways, Galadriel and the Fellowship are polar opposites.
As they leave, she gives a series of gifts, the most personal of which go to Aragorn, Sam, Frodo, and Gimli. Aragorn gets a sheath for Andúril and a brooch shaped like an eagle, with a green stone that comes from Arwen. Sam gets a box of earth from Galadriel's garden, which will bring life to his gardens back home. As he requested, Gimli gets a single strand of Galadriel's hair to set in crystal. And Frodo gets a crystal pendant from which shines the light of Eärendil, the Evening Star. We feel a little sorry for Legolas, Merry, Pippin, and Boromir: Legolas gets a Galadhrim-style bow and arrows, and the other three get belts. Not much compared to the light of Eärendil!
Galadriel just has to look at you to know your moral character. She’s psychic, which is deeply unsettling for all the members of the Fellowship. But the one who comes off the worst in Galadriel’s eyes is Boromir. She figures out that he is the least trustworthy member of the Company just a few chapters before Boromir falls under the power of the Ring and tries to grab it for himself.
Galadriel's clear sight may be the gift of Nenya, the Ring of Adamant. Yes, like Frodo, Galadriel is a Ring-bearer; but her Ring is one of the Three Elvish Rings of Power, and therefore has no taint of Sauron.
One last note about Galadriel's abilities: Galadriel has a basin of water she calls the Mirror of Galadriel. In it, one can see visions of things that may or may not come to pass. Sam sees the Shire all torn up, with a big factory chimney and the Hobbits being forced to work. He almost gives up the Quest right then and there, but Galadriel warns him that the Mirror may not show the truth. Frodo looks into the Mirror and watches the Eye of Sauron searching for him. Frodo feels the Ring growing heavier and heavier, until he almost slips into the water. But Galadriel stops him: she knows that he sees the Eye of Sauron, and that Sauron would like to catch a glimpse of both Frodo and Galadriel. But here, they are still safe. Galadriel keeps Lothlórien as a stronghold, but, as Haldir has pointed out, it is becoming an island in the middle of enemies.
Nenya can only help Galadriel keep the peace for so long: she knows that, if Sauron falls, her people will diminish and go into the West. Despite her regret, Galadriel wishes, "That what should be shall be [... the Elves] will cast all away rather than submit to Sauron" (2.7.97). She, like Elrond, is willing to pay the price for Middle-earth's safety from Sauron: that her own people will fade. This willingness to submit to fate for the greater good is why Elves often appear better and wiser than ordinary mortals.
Galadriel is not the only one testing people’s morals in Lothlórien. Frodo tests her ethics in turn, by offering her the One Ring to use as a force of good in the world. For a moment, she seems to consider the idea, imagining herself "[f]air as the Sea and the Sun and the Snow upon the Mountain! Dreadful as the Storm and the Lightning! Stronger than the foundations of the earth" (2.7.100).
But like Aragorn and Gandalf before her, she refuses Frodo's offer. She knows that she would start out doing good, but she would soon be corrupted by the unlimited power. Her refusal to take the Ring marks her as a true member of the Wise. The problem with the Ring is, the minute you admit you want it, you prove that you are too weak and greedy to carry it.
Galadriel's up-close-and-personal knowledge of the Rings of Power makes her an excellent person for Frodo to confide in. This chapter in Lothlórien is one of the last points in the series when Frodo actually gets to talk to someone more knowledgeable than he is. Galadriel, like Elrond and Gandalf, becomes a mentor for Frodo.