The handkerchief was the first gift Othello gave Desdemona and is a token of his love for her. According to Othello, the sacred handkerchief belonged to his mother and was given to her by an Egyptian sibyl. His mother instructed him to give the handkerchief to his wife and Othello believes that it represents marital fidelity. Desdemona cherishes the handkerchief and takes it with her wherever she goes.
Unfortunately, Desdemona unknowingly drops the handkerchief and Emilia discovers it. Emilia knows that her husband has been asking for the handkerchief and proceeds to give it to him. Iago then uses the handkerchief to his advantage in his scheme to destroy Othello. Iago places the handkerchief in Michael Cassio's room and tells Othello that he saw Cassio wipe his beard with Desdemona's handkerchief.
Iago continues to manipulate Othello by having him witness Cassio giving Desdemona's handkerchief to Bianca, which presumably proves Desdemona's infidelity in Othello’s eyes. The handkerchief is a significant plot device that confirms Othello’s suspicions that his wife is cheating on him with Michael Cassio. While it is nothing more than circumstantial evidence, Othello views it as proof that Desdemona is unfaithful and becomes motivated to kill her.
The handkerchief, or "napkin" as it is often called in the play, is a central plot device in Othello. Essentially, Iago uses the handkerchief to convince Othello that Desdemona has been unfaithful to him with Michael Cassio. Iago gets the handkerchief when Emilia, his wife, picks it up after Desdemona drops it. The handkerchief was Othello's first gift to Desdemona, and so it serves as a symbol of their love and her loyalty to him. The scheming Iago determines to drive a wedge between Othello and his wife by placing the handkerchief in Michael Cassio's room, and arranging for Othello to find out. After talking with Iago, Othello asks his wife for the handkerchief, which, he says, came from Egypt, where it was woven with silk from sacred worms and embroidered with berries dyed with the blood of mummified virgins. When Desdemona admits that she does not have the handkerchief, Othello is outraged. When it is revealed that Cassio (through the schemes of Iago) has come into possession of it, Othello assumes that Desdemona gave it to him. Iago pushes the scheme even further by making Othello believe that Cassio's comments about Bianca, his mistress (to whom he gives the handkerchief) are actually about Desdemona. The fact that Desdemona consistently advocates for Cassio before her husband (at Cassio's behest) only adds to Othello's suspicions, which eventually reach a boiling point. So the handkerchief is the plot device that Shakespeare places at the center of the fatal and tragic split between Othello and Desdemona.