What are the themes of Shakespeare's Othello?
Most obviously, the play is about jealousy and the damage that jealousy can do to a relationship. In the play jealousy is a "green eye monster that mocks the meat it feeds upon." At the heart of the play, we have two jealous men, Iago who is jealous because he is jealous, and Othello, is becomes inflicted with the "poisonous mineral" because of Iago's lies and machinations.
But the play is also about the way men view women: the tendency to view women as prizes that are won, and women's infidelity as attacks on their pride. This inability to see women truly without generalization and without stereotyping is a central idea of the tragedy.
Another theme is the insider/outsider theme. Othello's race, while not a factor in his achieving prestige as a military man, makes him feel insecure in his marriage. "Haply for I am black" Othello cries, and when comparing himself to Cassio, who is one of the "curled darlings" of Desdemona's country, he feels as if he has lost her. Part of Iago's manipulation of Othello is to make him feel as if he is an outsider to Venetian society.
And of course as is common with Shakespeare, the play explores the appearance versus reality idea. "When devils with the blackest sins put on, they do at first with heavenly shows as I do now," Iago boasts. Iago, clearly the devil of the play, is seen by every major characters as honest, honorable, and trustworthy. Desdemona, who is clearly the angel of the play, is viewed as deceitful and ungrateful by her father and a whore by her husband.
Another theme in the play could be honor and honorable action, especially as it concerns members of the military, who often consider themselves a "band of brothers."
Iago is able to win both Cassio's and Othello's faith and trust in his word as truth, possibly because they serve together in the military, and this creates the belief that they will always act with each other's best interests at heart. So, Iago is able to connive Cassio into drinking more than he should and then into appealing to Desdemona to help him win back his place, taken from him by Othello for instigating a drunken brawl.
He is also able to win Othello's confidence and trust, because he has been his ancient and served him faithfully through many battles. Iago is assumed to be honest by Othello, maybe not so much because he knows him as a civilian person, but because he has seen how he behaves in battle.
So military honor and how it operates in the ways that the men see each other is also a theme of the play, one that colors the men's judgement of each other.