This whole scene epitomizes Emilia's naivety and ignorance at this point in the play. She's openly lamenting the fact that Othello has just called Desdemona a whore and slapped her in public. Why is he behaving like this? And where on earth did he get such a terrible, slanderous notion? Whoever gave him this idea is an "eternal villain."

Unbeknownst to Emilia (and this is where the dramatic irony comes in), the dastardly villain she's describing is actually Iago, who pretends to be outraged at Othello's actions. Because Emilia is so utterly loyal and devoted to her husband, she hasn't the faintest idea that he's responsible for sowing the seeds of jealousy in Othello's mind. She still thinks Iago is a great man and a loyal servant who will do anything for his master. How little does she know.

The dramatic irony of this Act not only emphasizes the fact that Emelia is describing her own husband that she does not know has masterminded the jealous plot that has caused the death of her maiden, Desdemona, but it also points out that Emelia has unknowingly participated in the deadly plot by stealing the prized handkerchief from Desdemona and giving it to Iago.  This handkerchief is the catalyst that sets up the proof for Othello that Desdemona has been unfaithful with Cassio. Ironically, the audience (readers) know all of this, but poor Emelia is clueless.

This is dramatic irony because Emilia doesn't know that it is her husband, Iago, who is the villain she speaks of. She speaks harshly of a man who would do such a thing, calling him an "insinuating rogue" and a "cogging, cozening slave." We know this perfectly describes Iago (so perfectly, in fact, that some would question whether Emilia already knows it is Iago). As she says this, Iago is right beside her, saying "There is no such man; it is impossible," also ironic, for we know he is such a man.