He was probably of Durin's Folk.
Narvi was best known for his part in making of the Doors of Durin for the West-gate of Moria, on which Celebrimbor, an elf, wrote the inscription. He worked closely with the Gwaith-i-Mírdain; Celebrimbor in particular was his close friend. It can be implied that the relationship between Dwarves and Elves was neither pivotal nor had it yet subsided; Other than the age of the hall or the door, this also means Narvi lived during either the Early Days or the First Age.
Portrayal in adaptations
Shadow of Mordor
In the game Middle-earth: Shadow of Mordor, Narvi is mentioned as being the creator, or the one who commissioned, Celebrimbor's bow, Azkâr. After the player completes enough missions to forge the legend of his weapons, the game's description of the bow reads: "Azkâr. Narvi had me made for the ring-smith and for his loyal service. His arrows truly may they hit their mark [sic]."