Hook's sword is the weapon that Killian Jones once used to taunt a weak and cowardly Rumplestiltskin after stealing his wife. Centuries later, Emma Swan uses the sword to wake up Rumple after he enters a magical coma.
Before the Curse
Hook taunts Rumplestiltskin with his sword. ("The Crocodile")
After abandoning his post in the army, Milah becomes ashamed of Rumplestiltskin. Rumple returns home one evening to see Baelfire without his mother, so he decides to take his son out looking for her. Milah is found in a bar, drinking with pirates. Rumple tries to ask her home but she refuses, insulting Rumple as she does so. Bae then emerges and Milah changes her attitude, leaving with her son to protect him. Later that night, Rumple asks his wife if she'd really have liked him to die in the Ogre-Wars, she tells him that she just wishes he would have fought. The next day, Rumple is told that Milah has been kidnapped by pirates and he goes to the ship of Killian Jones to ask for his wife back, however, Jones refuses. He offers Rumple a duel in exchange for his woman but Rumple doesn't rise to the challenge. He is laughed from the ship. ("The Crocodile")
After the Third Curse
Hook's sword is destroyed to wake up Rumplestiltskin. ("Siege Perilous")
Emma entices Hook to meet her on his ship by ordering lunch for the two of them, proceeding to lay a table with her magic while at the same time transforming her look to that of what she wore on their first date. He tries grilling her for information but she refuses to divulge anything, instead proceeding to shock him by suggesting that they continue with a functional relationship. She uses Mr. Gold as an example, for Belle loved him in spite of the darkness, and goes on to say how she's stronger now than before, just like how Rumple stopped being a coward. Hook assures her that Rumple was a good man who he, as a pirate, taunted with a cutlass, having held it to his throat; he is the only one in that story who changed for the better, for Rumple became evil. Emma leaves the pirate with an ultimatum: he can say he doesn't love her, and she will go. He makes it explicit that he loved her, leading her to teleport away. Unbeknownst to him, however, she took his cutlass with her, because the missing ingredient to the healing potion needed to wake Mr. Gold is something that touched him before he was the Dark One. The cutlass provides this, and he awakes in Emma's lair. She explains to him that his heart is now a blank slate, which means she can mold him into the purest hero who ever lived, and then he can pull the sword from the stone. ("Siege Perilous")