Honesty is tied to Iago and his reputation. It is the realm of men, not women (who are characterized by its opposite: "dishonesty" and "unfaithfulness").
"Honest" is used 52 times in the play. Nearly everyone in the play publicly calls Iago honest, even Iago himself. About half the time it is used to refer to Iago. It is his self-fullfilling prophecy and one of the great epithets in all of literature, especially since Iago says from the very beginning of the play, "I am not what I am." In other words, I am not an honest man.
Most famously, Othello says:
Everyone thinks he's honest: Othello, Emilia, Roderigo, Desdemona. The two characters that are closest to him, Emilia and Roderigo, still confide in him, knowing this! Roderigo continues to fill his purse, knowing that he is a dishonest villain. Emilia steals Desdemona's handkerchief for him, knowing that he will hurt her with it.
By having others label Iago as honest, it gives him free reign to play a duplicitous role in his marriage, against the Moor, and against Desdemona with his henchman Roderigo.