The Elven Gifts from Lothlorien were special Elvish items given to the remaining members of the Fellowship of the Ring by the Lady Galadriel and the Lord Celeborn. Each member of the Fellowship was given a personal gift.
For Frodo Baggins - The Light of Eärendil - A small crystal bottle of liquid, it contains the light of Eärendil's star in the water of Galadriel's fountain. The phial emits a brilliant light in darkness.
For Samwise Gamgee - Earth from Galadriel's Orchard and a Mallorn Seed - These are contained in a small box of grey wood with a silver G-rune on the lid. He uses it to replant trees in the Shire after the Scouring of the Shire. In the movie, Sam instead receives Elven rope. This rope is much stronger than other rope. In the movie, as in the book, the rope allows itself to be retrieved from its anchorage with a small tug, due to the Elvish skill at rope-making.
For Aragorn - Elven Scabbard- A magical scabbard, any sword sheathed in this scabbard will never break. And Elessar the Elfstone - A green gem set in a silver eagle shaped brooch, left for him by Arwen. In the movie, Aragorn does not receive either of these, as Arwen has already given him the film's equivalent gem; Elrond will later present him a scabbard with Andúril, though no indication is given that it is magical. Instead, Celeborn gives him a curved Elvish hunting knife.
For Gimli - Three Strands of Galadriel's hair - Overwhelmed by Galadriel's great beauty, Gimli could think of nothing else he wanted but a single strand of her hair. Galadriel gave him three. Gimli wished to encase this gift in imperishable crystal, as an heirloom of his house and a sign of good will between the Dwarves and Elves.
For all the Fellowship of the Ring (characters) - Elven Cloaks - It is worth note that The Fellowship received Elven cloaks from Galadriel which helped hide them from unfriendly eyes. The cloaks were personally woven by Galadriel and her maidens. The brooches were in the form of a green leaf veined with silver. The only notable exception to those who didn't receive a cloak was Gandalf, who at the time, was presumed dead at the hands of Durin's Bane. In the film, after defeating the Balrog and returning to the world of the living, Gandalf appears in Fangorn with a brooched cloak, implying that he traveled to Lorien before joining up with scattered members of the Fellowship.