What was lady Galadriel's gift to Frodo in The Fellowship of the Ring?

Galadriel gave Frodo the Phial of Galadriel in "The Fellowship of the Ring." It was a small crystal vessel containing water from her fountain and the light of Eärendil's star.

The gift was presented when the Fellowship departed Lothlórien, the Elven realm ruled by Galadriel and Celeborn. Galadriel told Frodo that the phial could be a light in dark places when all other lights went out. Its light ultimately came from Eärendil, whose Silmaril shines in the heavens and preserves a connection to the ancient light of the Two Trees of Valinor.

The phial becomes especially important in Mordor. Frodo and Sam use it near Cirith Ungol to illuminate the darkness, and Sam later raises it against Shelob, whose lair is otherwise nearly impenetrable. It is sometimes casually called a vial or star-glass, but "the Phial of Galadriel" is the canonical name. The dagger, arrows, belt, and other gifts went to different members of the Fellowship.