One of the thirteen Dwarves of the Blue Mountains who set out to reclaim the Lonely Mountain from Smaug, under the leadership of Thorin Oakenshield. Nori seems to have been the brother of Dori (based on the similarity of their names, and the sharing of purple hoods). Both Nori and Dori were capable flautists, and seem to have carried their flutes with them. Both these apparent brothers also shared Bilbo's liking for regular meals.
Fíli and Kíli were known to be the youngest of Thorin's companions by some fifty years. The elder brother, Fíli, was born in III 2859, so Nori must have been born at least fifty years before that date.
Like many other Dwarves in Tolkien's work, Nori's name comes originally from the Old Norse poem Völuspá. The translation is not certain: various sources suggest different interpretations, included 'little scrap', 'turner', or 'shipper'. Given that Dori has a name that seems to mean 'borer', then 'turner' probably makes most sense in context.