Conan's Sword is a mighty and fine weapon forged by Conan's father from Star Metal, regarded by the Blacksmith as his finest piece of work. He forged it for his son but Conan could only have it when he was "man enough" (strong enough) to earn it, and placed it within a container of heavy stone that even the Blacksmith had trouble opening.
When Conan had grown up, the wicked wizard Wrath-Amon attacked the Cimmerian village, seeking the Star Metal Conan's father had used to make all kinds of weapons. When the Blacksmith said there was no more, Wrath-Amon ordered his Serpent Men soldiers to destory the village and find any Star Metal they could.
Conan went to get his sword, and, having grown older, stronger, and motivated to protect his village and family, he successfully opened the container (even lifting the stone lid and throwing it aside, showing he had become even stronger than his father) and at last claiming his sword.
Although he chased off the wizard, Wrath-Amon used his evil magic to turn Conan's family into stone. He swore no matter what he would restore his family to flesh and blood.
Conan's Sword has been his most relied-upon weapon and tool in his quest, as well as a target of his enemies, especially Wrath-Amon, who would love nothing more than to take the sword and corrupt it before Conan's eyes.