After a brief conversation with Othello, Iago awaits Cassio's return. He intends to talk to him about Bianca, without explicitly saying her name so Othello, who is lurking in the shadows, will believe that they are talking about Desdemona.
Cassio enters and Iago calls amiablely to him.
Iago askes him about the woman he has been seeing and Cassio begins to laugh. Iago asks if Cassio means to marry her, to which Cassio responds with "I marry her? What, a customer?" Here he calls, who he assumes to be Bianca, a whore. This enrages Othello who is still listening into the conversation.
Bianca enters raving about the handerkchief and says "Let the devil and his dam haunt you! This is some minx’s token, and I must take out the work! There, give it your hobbyhorse!" For Iago, this situation could not have played out better. Not only has Bianca's presence confirmed that Cassio has Desdemona's handkerchief, but it makes him look like more of a player.
Cassio, who had just been trying to enjoy a conversation with his buddy, all of a sudden has to deal with this woman he has been having relations with.
Bianca storms off, and Iago advises Cassio to go after her, lest she go shout about him in the streets. Cassio exits and Iago briefly reflects to himself how well this all worked towards his plan.