The sword, specifically the one that is owned by Theseus, is mentioned on the first page of the text as Theseus says he “wooed” Hippolyta with it, and now they are to be married. However, it has a lot more meaning in the play than just that, and the meaning of Theseus's comment also isn’t cut and dry.
Right from the start, Theseus says, “I wooed thee with my sword” (1.1 17 ). Having a sword woo someone can have multiple meanings. One, which is the literal meaning, is that Theseus has such skill with a sword that when Hippolyta saw him use it, she fell in love with him. Another interpretation of how the sword wooed Hippolyta is that Theseus fought and beat the Amazons, which was a group of warrior women of which Hippolyta was queen. Then after beating the Amazons, he decided to have her for his wife, and he took her. This seems like a more likely possibility because the Amazons did not want to be subjected to the power or wills of men. Especially since Hippolyta was queen, marrying Theseus would give her less power. This power dynamic is exemplified in A Midsummer Night's Dreamright after Theseus mentions wooing Hippolyta. Hippolyta was become quiet and does not say anything when Egeus brings up his case with Theseus. This shows that she had no power and that the wooing was probably more like conquering. As a result, Theseus is extremely happy about the relationship, which is shown by his excitement for their upcoming wedding: “I will wed thee in another key, / With pomp, with triumph, and with reveling” (1.1 19-20). While on the contrary, Hippolyta is dreading her marriage as she does not like Theseus, which is exemplified by the way that she is quiet.
In the beginning the sword is described as wooing Hippolyta, which is not a sword’s purpose. A sword is meant to kill. And this image helps us thing about how no relationship is ideal in the play. There is no relationship between Demetrius and Helena. Hermia and Lysander are being blocked from their love. And Hippolyta is forced into her marriage. Even the fairy king and queen have their issues, fighting over the little boy. Oddly, at the end, when a sword is used for its purpose, to kill (Pyramus and Thisbe in the play within the play commit suicide), all the relationships seem better. Hippolyta and Theseus bond over dogs, and now they have conversations and Hippolyta is talking more. Then Lysander and Hermia are together, and Helena and Demetrius are together (even though it’s through the love juice). Finally, Oberon and Titania are dancing and happy together. The transition away from wooing with a sword marks the transition from conflict and confusion in the beginning to everything working out.