Othello is giving Iago important papers to remind the audience that Othello is a general. It also shows that Othello trusts Iago more after Cassio lost his spot.
These letters give, Iago, to the pilot and by him do my duties to the Senate.
Cassio is talking to Desdemona about how she should help him get his lieutenancy back by having her talk to her husband. Desdemona, being the nice innocent person she is, says she will try her best. This is part of Iago’s master plan to get Othello jealous by having him think his wife loves Cassio.
His bed shall seem a school, his board a shrift.
Iago is talking to Othello about Desdemona’s affair with Cassio. Othello asked for proof that she is being disloyal but Iago only has verbal evidence. Iago says it’s only a dream but even this makes Othello start to go mad as Iago wants.
In sleep I heard him say “Sweet Desdemona, let us be wary, let us hide our loves.”
Othello is telling Iago he wants to kill Cassio and Desdemona. Othello wants Iago to help him to get his revenge and makes Iago his lieutenant. Iago has completed half of his revenge.
I am your own forever.
For the fair devil. Now art thou my lieutenant.
Othello is confronting Desdemona that she does not have the handkerchief that he gave her. Othello believes that the handkerchief has magical powers that help bind him and Desdemona. When she says she does not have it, Othello is almost 100% sure she is in love and having an affair with Cassio.
Lend me thy handkerchief
Fetch ‘t. Let me see it
I have it not about me. I say it not lost.
Desdemona is talking to Emilia about how Othello is so worked up about her handkerchief. Desdemona does not know that Othello thinks she is cheating on him with Cassio. She is completely out of the loop and is confused. Emilia tells her that jealousy is like a monster that grows and grows out of nothing. Desdemona hopes the monster of jealousy does not consume him.