The Elven Ring worn by Galadriel was Nenya, also called the Ring of Water or the Ring of Adamant. It was one of the Three Rings made for the Elves during the Second Age.
Nenya was forged by Celebrimbor and the Elven-smiths of Eregion. Unlike the One Ring and the other Rings of Power, the Three Elven Rings were not made directly under Sauron’s guidance, although their power remained connected to the One Ring. Nenya was made of mithril and set with a white stone.
Celebrimbor entrusted Nenya to Galadriel after Sauron attacked Eregion. She used its power to preserve and protect Lothlórien, helping the realm retain its beauty and resist the corruption spreading through Middle-earth. In the book, Frodo could perceive the ring because he was the Ring-bearer; Sam saw only a light shining from Galadriel’s hand.
Narya, the Ring of Fire, was ultimately worn by Gandalf, and Vilya, the Ring of Air, was worn by Elrond. The Ring of Barahir was a different heirloom associated with Aragorn’s ancestry, not one of the Three Elven Rings.