Barahir's father was Hador, a famously long-lived Man who ruled Gondor as its Steward for no less than one hundred and seventeen years. According to the best sources we have, Barahir was born in the twelfth year of his father's rule, meaning that he succeeded Hador at the age of one hundred and five. Given Barahir's great age, it is not surprising that his rule, and that of his son Dior, were brief ones.
Barahir held the office of Steward during the waning years of the Watchful Peace. Both he and his son Dior, then, enjoyed rules free of troubles. Barahir's grandson was Denethor, the son of his daughter Rían, who was a young noble of just twenty at the time Barahir became Steward. It was Denethor who was destined to rule Gondor at the time that war erupted on its borders, more than sixty years after Barahir's death.
Barahir ruled as Steward for seventeen years, and was succeeded by his son Dior.
The date of Barahir's birth appears only in The History of Middle-earth volume 12, The Peoples of Middle-earth. It cannot therefore be considered completely reliable.