This line shows Iago as the most jealous character in the play. He is not jealous for true cause but as Emilia declares, jealous because he is jealous. He suspects Othello is sleeping with his wife. He later suspects that Cassio has been with his "nightcap" too. But in neither case does Iago try to find out the truth. He "knows not as if for surety, but will act in mere suspicion." In other words, Iago is interested in revenge; he is not interested in evidence. It's almost as if Iago has to convince himself that these two men are hurting him, so that he can justify what he is planning to do to them. In Act 5, Iago comments that Cassio has a "daily beauty in his life that makes me ugly." This line is a key to understanding Iago's motivation. He cannot abide the happiness, the good fortune, the beauty in other people's lives, and sees it as a sport to bring misfortune to their lives.
In his first soliloquy, Iago says: “It is thought abroad that ’twixt my sheets / He has done my office” (I.iii.369–370). This is one of the reasons that Iago gives for justifying his revenge against Othello.
We think, because he says it in soliloquy, that Iago is telling the truth. I doubt it. It is doubtful that Othello would desire Emilia, an older married woman, of lower social standing, not known for beauty. No, Desdemona was his focus. She was all this and the daughter of a Senator. Desdemona was Othello's prize.
Iago is paranoid. He is using this obvious racist fear (that a black man is a better lover than a white man and, therefore, able to seduce the white man's woman) as a means of rationalizing his revenge plot. In this way, he is convincing the predominately white European audience to join him in his racial fear. He is seducing us the way he fears that either Othello has seduced Emilia or Emilia let herself be seduced by the Moor.
The key to understanding Iago is that he hates. We are never given, within the context of the play, solid reasons; his statement that the "Moor has done my office," referring that his wife Emilia and Othello may have bedded, may or may not be true, although much later in the play Emilia admits to Desdemona she would go quite far to advance herself or her husband. Throughout the play, reference is made to the devil, and in the last act Othello intimates that Iago is precisely that. He thrives off the misery he has created, and the play is about him targeting Othello and taking him down and out simply for the evil pleasure of doing so. Any excuse or reason he can distort that furthers his cause will be employed. He hates Othello simply because Othello is virtuous, and he is not.