Michael Cassio is very courteous towards Desdemona. This is because he wants her to intercede with her husband Othello on his behalf. Cassio recently got into an unseemly drunken street brawl, for which he was dismissed from Othello's service. As Cassio is desperate to get back into the Moor's good books, he asks Desdemona to put in a good word for him.
So one day, he comes round to see Desdemona when she's alone. As expected, Desdemona agrees to do what she can to help. The meeting between Cassio and Desdemona is very pleasant and friendly, and Cassio leaves, believing that he will soon be reinstated in Othello's service.
As Cassio is leaving, Othello and Iago are just arriving. When Iago sees Cassio leaving Desdemona's apartment, he immediately hits upon a cunning idea. He's going to convince Othello that Cassio and Desdemona have been having an affair. Of course, Iago doesn't come right out and say that he thinks that Desdemona's been cheating on Othello; he's much too clever and subtle for that. Instead, he uses innuendo to sow doubt in Othello's mind, expertly playing on the Moor's deep-seated insecurities about his race and social status to convince his master of his wife's infidelity.