First, Othello loses the handkerchief. He says to Desdemona, "Let it alone." He will later blame Desdemona for losing it. As the napkin is a symbol of his love for his wife, he sabotages his own marriage by setting her up for failure.
Emilia finds the napkin and admits that her husband has wanted her to steal it. Why does Emilia give it to him? Is she too jealous of Desdemona and Othello's love? Is she not lacking in that department in her own marriage? She thinks the napkin will help regain her status in Iago's affections. Iago gives her a few crumbs from his table: "A good wench," he calls her. She's a fool, like Roderigo.
Iago starts to prove Cassio and Desdemona are cheating. The first story is a weak one: Iago says Cassio sleep-talks about Desdemona. Very Freudian.
Othello isn't yet convinced; he wants "ocular proof." Knowing this, Iago plants the idea that Desdemona has given the napkin Cassio. So overcome by jealous rage upon hearing this, Othello loses his power of speech. He has a bunch of one liners:
"Death and damnation! O!";
"Give me a living reason she's disloyal";
"O monstrous! monstrous!";
"I'll tear her all to pieces;"
"O, blood, blood, blood!"
His language, which helped him defeat Brabantio and Iago in court and on the street, is gone now. He had avoided using his hands in combat in Venice; now, his hands will become weapons against his voice and logic. Now, he is a man of action, a man of passion, a man of combat--a soldier again. But, he has misidentified his enemy: he thinks it's Desdemona, but it's really Iago and himself.
If I may go a bit beyond line 445 (seems kind of pointless not to, as the scene ends at line 533 anyway)....
At the end of the scene, Othello basically divorces Desdemona and marries Iago. Only Iago says the "marriage" vow: "I am your own forever." This stands in sharp contrast to what he said in Act I: "I am not what I am."