Why is it ironic that Othello doesn't believe Emilia when she tells him Desdemona is innocent?
Emilia declares Desdemona's innocence at the opening of Act IV, scene ii. Othello is grilling her as to whether she has seen anything between Desdemona and Cassio, and finally Emilia says:
I durst, my lord, to wager she is honest,
Lay down my soul at stake: if you think other,
Remove your thought, it doth abuse your bosom;
If any wretch ha' put this in your head,
Let heaven requite it with the serpent's curse...
The irony here, in the lines I have bolded, is that she is referring to exactly what has happened. The audience knows this to be true, since they have seen Iago work his evil "serpent's curse." So, it is dramatic irony as well, as Othello does not know what the audience knows, that Emilia speaks the truth about the "wretch" who put the idea of adultery "in [his] head."
It is also a great moment to wonder how much of what is happening Emilia suspects (or actually knows). If she does know what's going on, it is hard to see her as so loyal to Desdemona as she professes to be.