The three rings gifted to the Elves are the only rings we actually know of by specific names: Narya, Nenya, and Vilya. Narya, the ring of fire, was gifted to Círdan, the lord of the Grey Havens, the port city that many Elves departed from Middle-earth to the Undying Lands. It’s fitting, then, that among its magical abilities were its powers to stave off the weariness of age, as well as inspire hope in people around the ringbearer—and perhaps even more fitting then that Círdan eventually gifted the ring to Gandalf, recognizing that the wizard was actually one of the angelic Maiar, believing it better in his hands for the trials the world was about to face.
Nenya, the ring of water, was gifted to Lady Galadriel, who bore it to safeguard the forests of Lórien from incursion. While never explicitly specified, the ring—described as gleaming like a star so bright that only other ringbearers could see its true nature—was said to have powers of protection that sustained the forests around Lothlórien, keeping as much of the forces of darkness out as possible.
Lastly, Vilya, the ring of air, was gifted to Gil-Galad, the High King of the Ñoldor Elves. The most magically powerful of the three Elven rings, Vilya’s specific powers were unknown, beyond that Celebrimbor himself specified that all three rings had healing and preservative powers, unlike the other rings of power. After Gil-Galad died at the foot of Mount Doom in the Battle of the Last Alliance in the Second Age’s climax, Vilya was inherited by Elrond of Rivendell, who wore the ring until he passed into the Undying Lands at the end of the Third Age.