Nayru was one of the three Goddesses that created the land of Hyrule and the Triforce in The Legend of Zelda series, along with Din and Farore who were the three beings that created Hyrule and the world, Nayru's role in the creation was water, law and skies.
At the dawn of time, Nayru, along with Din and Farore, descended upon the chaos that was to become the land of Hyrule, each of them creating a different facet of the realm. According to The Legend of Zelda: Ocarina of Time, Naryu, "poured her wisdom onto the earth and gave the spirit of law to the world". Upon departure, they created the Triforce, the essence of their power, and left it under Hylia's protection.
The Legend of Zelda: Ocarina of Time
in Ocarina of Time, Nayru is depicted as a golden figure surrounded by a blue aura and is firstly described as such by the Great Deku Tree. She appears once again in the scene described by Princess Zelda upon her first meeting Link.
The Era without a Hero
During The Era without a Hero, Nayru along with the others gods heard the pleas of the people of Hyrule who were faced by Ganon's onslaught of evil, instructed them to flee to Hyrule's mountaintops in order to escape the apocalypse they were about to unleash upon the land to halt Ganondorf's invasion by sealing him under The Great Sea along with the kingdom of Hyrule.
The Legend of Zelda: The Wind Waker
During the events of The Legend of Zelda: The Wind Waker Nayru is only seen as a statue which open the path to the Tower of the Gods once given the matching pearl obtained from Jabun near Outset Island.
The Legend of Zelda: Twilight Princess
During the events of The Legend of Zelda: Twilight Princess, the light spirit Lanayru tell the tale of the creation of the kingdom of Hyrule by the three Goddesses and explain how him and the others light spirits were ordered to seal the power that the Dark Interlopers were using against Hyrule. The Goddesses are also said to have banished the said interlopers into the Twilight Realm. Nayru's likeness also appears depicted in the giant Triforce monument located in Hyrule Castle's trhone room.
The Legend of Zelda: A Link to the Past
In The Legend of Zelda: A Link to the Past Nayru is only mentioned in the game manual describing the creation of Hyrule and is said to be the "God of Wisdom" before being renamed to a "deity" in the The Legend of Zelda: A Link to the Past & Four Swords version to fit the Ocarina of Time version.