Nymeria was adopted as a pup with the rest of the Stark direwolves when Eddard Stark and his entourage came upon the pups and their deceased mother. At the request of Jon Snow, the pups were spared and each Stark child adopted one as their own. Arya names her direwolf after a fearsome warrior-queen.
Nymeria is faithfully loyal to Arya and defends her against Prince Joffrey Baratheon by biting his arm when he attempts to strike Arya with a sword. Arya, fearing for Nymeria's well-being, forces her to leave. After the incident, Queen Cersei Lannister orders the death of Nymeria, however as she is nowhere to be found, Sansa's direwolf Lady is killed in her place.
Nymeria is currently running loose somewhere in the Riverlands, her exact whereabouts unknown.
In the A Song of Ice and Fire novels Nymeria is an exuberant and playful wolf, but is also fiercely defensive of Arya Stark. Arya names Nymeria for the warrior-queen of the Rhoynar who led her people to safety in Dorne, a thousand years before the events of the series.
According to the TV series official pronunciation guide developed for the cast and crew, "Nymeria" is pronounced "Nigh-MEER-ee-uh", as opposed to "Nih-MER-ee-uh".