Dramatic Suspense!

Contrast the amount of information possessed by the audience as the play proceeds with the knowledge that various other characters have: what is the effect of such a contrast?

This is pretty obvious. Poor Othello is so out of the loop. In Act III, Iago has multiple conversations with different people, so the audience knows all sides of the story. In his asides or conversations with Roderigo, he reveals that he is not the "this fellow of exceeding honesty" (III.iii.259) that he claims to be.

But Because Othello believes Desdemona is cheating on him and Desdemona has no idea, suspense is created. Will Cassio and Desdemona live? (More importantly, will Iago DIE?)

Iago's extreme jealously has driven him to frame a good man against Othello, which will ruin many lives..

Desdemona is "most unhappy in the loss of the [handkerchief]" (III.iii.95) but Emilia does not say anything about it, which is really annoying. She has the power to fix it, if she would just tell Desdemona about Iago stealing it.