At first, Barbantio, Desdemona's father, accuses Othello of using withcraft to win his daughter's love. He has his men capture Othello and plans to bring the case before the Duke in court. However, Othello later reveals the real reason why Desdemona fell in love with him and says that she will confirm his story. Othello is an accomplished officer and solder with a mysterious past. He says that when Barbantio invited him to visit and share his many war stories, Desdemona overheard, and the stories caught her interest. He says that she asked him to retell the stories to her, and when he did, she fell in love with him.
In short, she agrees to marry him because of his mysterious and heroic stories.