The significance of the handkerchief is their bond of marriage and keeping them together as one. Every time Othello asks Desdemona about the handkerchief, she deny's the loss and to present in front of him. For Othello that think meant a lot, like their bond, trust, faith and etc. The explanation Othello gave to her made her say that she never had it or gotten from him. That was given by a witch to Othello's mother to give it to Othello's wife; that is a magical handkerchief, there is a spell in it and, that is to keep a marriage together and if its lost or anything the marriage starts to fall apart and breaks he bond. Now we can see t hat there marriage is going to a rough path and there is no more trust or faith from Othello's side.