You thought there was going to be a battle scene. Instead, it turns out that a really big storm knocked out the entire Turkish fleet, so now Othello will have nothing to do except honeymoon in Cyprus.
Cassio has arrived before Othello and now converses with the Governor of Cyprus, Montano, about how wonderful Othello and his new wife are. As they await everyone else's arrival, the people onshore in Cyprus are nervous about whether Othello and Desdemona made it through the storm. Cassio hopes they'll both get to Cyprus safely and quickly.
Desdemona makes it to Cyprus first, along with Iago and his wife, Emilia, who is going to be Desdemona's lady attendant. Cassio welcomes Desdemona and Emilia—flirtatiously kissing Emilia. Iago quips that if Emilia would kiss Cassio's lips as deftly as she whips him (Iago) with her tongue, Cassio would be over her quickly.
As Iago mocks his wife for being a nag, Desdemona tries to defend her. Desdemona then asks Iago his opinion of women. Iago goes through a series of rhyming racist and sexist jokes. At least we see where Iago stands.
Iago makes a snide aside to himself, noting how freely Cassio flirts with the women, kissing them and taking their hands to his lips. Iago will gladly make Cassio's hand-kissing his undoing. Iago then says after he's done his part, Cassio will wish his fingers were "clyster pipes" or enema tubes. (Gross!)
Finally, Othello shows up. He and Desdemona embrace and put on a big show of PDA (public display of affection). Othello says he could die now, as he's so happy to see Desdemona. "God forbid," Desdemona says. They engage in more PDA. After instructing Iago to get his trunks and take the ship's captain to the castle, Othello leaves with Desdemona.
With everyone else gone, Iago and Roderigo (who have traveled there together) are left to start scheming again. Iago says men in love are known to be more beastly than their natures usually allow, and he plans to take advantage of this.
Iago tells Roderigo that Desdemona is already over Othello and interested in Cassio. He then gives his longwinded speech, again, about how passions tend to cool. He says that as Desdemona got over Othello, Cassio stepped right in, since he's handsome and charming and valiant. Iago offers as proof the fact that Desdemona held Cassio's hand while they greeted each other, which is no evidence at all, unless you're a jealous, murder-plotting lover.
Conveniently, Cassio will be on the night-watch this evening, so Iago suggests that perhaps Roderigo would like to pick a fight with him, get him demoted, and then have less competition for Desdemona.
Roderigo agrees. After he exits, Iago gloats to the audience about the success of his scheming. He has actually convinced himself that it's perfectly possible that Desdemona and Cassio might have an affair.
Iago admits that Othello is a loving husband to Desdemona, but says that he, too, loves Desdemona. Don't forget, the revenge bit seems to stem from Iago thinking Othello had sex with his wife Emilia. He doesn't know for sure, but he's going to assume it's true, as that makes life and crime easier. The thought (of Othello with Emilia) plagues Iago, and he won't be content until he's even, "wife for wife." (This might suggest that Iago wants to defile Desdemona by sleeping with her, or some other means.)
If he can't explicitly ruin Desdemona, Iago will be contented by making Othello so jealous he can't think straight. If Roderigo does his job right (and picks a fight with Cassio), then Iago can use Cassio as a means to exploit Othello's jealousy. Iago plans to trash-talk Cassio to Othello, planting suspicion about Cassio's alleged relationship with Desdemona. Iago also clarifies that part of his hatred for Cassio is a suspicion that Cassio, too, has slept with Iago's wife.
Iago gloats that, despite all this wickedness, Othello will praise him and not realize he is the one orchestrating Othello's madness and downfall. Iago admits his plan isn't perfected yet, but evil never is—until the time comes for it to be done. Mwah-hah-hah.