Darkness was Lady Death's original sword and it was forged for her by Cremator, Hell's Blacksmith. It was forged to give her a weapon with which to slay her father, who had entered hell just before her intending to replace Lucifer as ruler of Hell. In her battle with Lucifer the blade breaks in two before reforming itself. She looses the blade for most of the "Between Heaven and Hell" arc regaining the sword from Lucifer right at the end.
Later Lady Death would use it to kill Lucifer (or so she thought) and rule over Hell. It is snapped in two in Asgard by one of Genocide's minions where Brock finds it's shattered hilt. He takes it to his forge and using a mold commissioned by Odin melts it down and infuses it with every spell he knows and can find, to make a new blade for Lady Death to use against Genocide.
The new blade he creates, he names Nightmare.