Root appears only in the 2004 film based loosely on the Earthsea books. He doesn't appear in Ursula Le Guin's stories.
In the film, he appears as a minister and senior advisor to the older Prince Of Enlad (Arren's father). He is an old man, encompassing years and years of wisdom. He reveals the story of Dragons and Humans' brotherhood as one.
He is a trusted elder and help of the Prince and is well-versed in the talk of the Balance.