The son of Húrin II, born soon after the settlement of Rohan (the Golden Hall of Meduseld was completed when Belecthor was twenty-four years old, so he may even have been a guest at the feast to mark its founding). He succeeded his father at the age of eighty-three to become Gondor's fifteenth Ruling Steward. His twenty-seven year rule was free of incident, or at least no annals of any significant events during his Stewardship have come down to us.
Belecthor was the ancestor of two lines of Ruling Stewards. He himself was succeeded by his son Orodreth, and Orodreth by his own son Ecthelion I, but Ecthelion produced no heir. Hence the line of the Stewards was reckoned back to Belecthor I, and passed to the descendants of his daughter Morwen. Egalmoth, Morwen's grandson, was the first Steward of this new line to take office.
The date of Belecthor's birth appears only in The History of Middle-earth volume 12, The Peoples of Middle-earth. It cannot therefore be considered completely reliable.
Belec- is presumably derived from beleg, 'great', but the -thor element is less certain. It typically relates to things which come rushing downwards (as in the river name Brilthor, 'glittering torrent'), and appears to be connected with the swooping of Eagles, so Belecthor might mean something like 'great one who descends like an Eagle'.
Belecthor's daughter Morwen is only named in volume 12 of The History of Middle-earth. The direct line of descent from Belecthor came to an end in III 2698 (forty-three years after Belecthor's own death) when his grandson Ecthelion I died without issue. It was the descendants of Morwen, in the person of her grandson Egalmoth, who continued the line of the Ruling Stewards.