In Shakespeare's tragedy Othello, Othello's wife, Desdemona, and Iago's wife, Emilia, have developed a close relationship. This is due primarily to Emilia's role as Desdemona's maid, but it's also due to the relationship between their husbands. Iago is General Othello's ensign or "ancient," and, more importantly, Iago is Othello's confidant. Ordinarily, a general and an ensign wouldn't have such a close relationship, but Iago has been at Othello's side through many battles, and he's won Othello's trust.
As the play progresses, Iago's role as Othello's confidant greatly impacts Emilia and Desdemona's relationship.
Emilia and Desdemona exchange a few words throughout the play, but it isn't until act 3, scene 4 that they have an actual conversation. The conversation doesn't tell the audience anything new about Emilia or Desdemona but simply reinforces what the audience already knows about each of them.
Emilia is worldly, practical, realistic, sexually experienced, earthy (if not downright bawdy), distrustful of others (particularly men), somewhat cynical and pessimistic, and she is not afraid to speak truth to her betters—which are the traits of many of Shakespeare's characters in similar roles.
Desdemona is naive about the world and men-women relationships, optimistic, idealistic, trusting to a fault (even of men like Iago), and, like many similar characters in Shakespeare's plays, destined to suffer greatly for her failure to see the world and the people in it as they truly are.
Even after Othello has humiliated her and slapped her in public, Desdemona still doesn't understand or choose to acknowledge Othello's intrinsically jealous and violent nature.
EMILIA: I would you had never seen him [Othello]!
DESDEMONA. So would not I. My love doth so approve him,
That even his stubbornness, his checks, his frowns—
...—have grace and favor in them. (4.3.19-22)
Desdemona seems blissfully unaware of the wrongs men and women do to each other.
DESDEMONA. ...O, these men, these men!
Dost thou in conscience think—tell me, Emilia—
That there be women do abuse their husbands
In such gross kind?
EMILIA. There be some such, no question. ...
DESDEMONA. I do not think there is any such woman.
EMILIA. Yes, a dozen, and as many to the vantage as would store the world they played for. (4.3.63-67, 88-90)
Desdemona is taken aback when Emilia admits that she, too, can be tempted to be unfaithful to her husband. Desdemona is equally taken aback to learn that Emilia might think that Desdemona capable of the same infidelity.
DESDEMONA. Wouldst thou do such a deed for all the world?
EMILIA. Why, would not you?
DESDEMONA. No, by this heavenly light!
EMILIA. Nor I neither by this heavenly light; I might do't as well i' the dark.
DESDEMONA. Wouldst thou do such a thing for all the world?
EMILIA. The world's a huge thing; it is a great price
For a final vice.
DESDEMONA. In troth, I think thou wouldst not.
EMILIA. In troth, I think I should, and undo't when I had done. (4.3.68-78)
The scene ends with Emilia's philosophy of infidelity between husbands and wives—a philosophy not unlike Shylock's rationalization in Shakespeare's The Merchant of Venice for taking revenge on Antonio for being a Christian.
EMILIA. ...But I do think it is their husbands' faults
If wives do fall; say that they slack their duties
And pour our treasures into foreign laps,
Or else break out in peevish jealousies,
Throwing restraint upon us, or say they strike us,
Or scant our former having in despite,
Why, we have galls, and though we have some grace,
Yet have we some revenge. Let husbands know
Their wives have sense like them; they see and smell
And have their palates both for sweet and sour,
As husbands have. What is it that they do
When they change us for others? Is it sport?
I think it is. And doth affection breed it?
I think it doth. Is't frailty that thus errs?
It is so too. And have not we affections,
Desires for sport, and frailty, as men have?
Then let them use us well; else let them know,
The ills we do, their ills instruct us so. (4.3.91-108)
Women are people, too, says Emilia. Women are neither better nor worse than men, and they have an equal right to behave as men do. The have an equal right to cheat on their husbands if they choose to do so, and particularly if their husbands cheat on them.
Emilia and Desdemona don't realize that this is the last conversation they'll ever have except for Desdemona's dying words to Emilia, which, true to Desdemona's character, reflect her optimistic, idealistic, and too-trusting nature.
EMILIA. Sweet Desdemona! O sweet mistress, speak!
DESDEMONA. A guiltless death I die.
EMILIA. O, who hath done this deed?
DESDEMONA. Nobody; I myself. Farewell;
Commend me to my kind lord. O, farewell! (4.3.145-149)