Isildur is the son of the Elendil, King of Gondor. On the Gorgoroth Plains during the Siege of Mordor , he saw his father struck down by Sauron. He then took up the shard of Narsil and cut the One Ring from Sauron's finger, which led to his defeat. Isildur then took up the One Ring. Elrond, who had been Gil-Galad's standard bearer, led Isildur into the Cracks of Mt. Doom to throw the One Ring in and destroy it, but Isildur had already been seduced by the Ring.
Isildur ignored Elrond's advice to destroy the Ring and instead kept the Ring for himself. Later, the Ring betrayed Isildur when he tried to use it to escape an ambush by Orcs at Gladden Fields near the River Anduin. It slipped off his finger in the river and the Ring was lost for years until Sméagol found it. In the time of Aragorn, Gondor had long been ruled by Stewards awaiting the return of an heir of Isildur. Boromir and Faramir are the sons of the current Steward of Gondor, Denethor II.
Aragorn, the last heir of Isildur, is reluctant to take on what is his birthright because of the weakness that Isildur displayed. Now faded into legend, the Ring has become known simply as Isildur's Bane and its true nature forgotten by all but a few.