Jealousy runs throughout Othello. Jealousy is both resenting someone else for their achievements, often because you feel you deserve what they have gotten, and wanting to guard what you have from others.
Iago's jealousy of Cassio for being promoted over him sets the plot in motion: Iago's anger at his talents being, in his opinion, underrated leaves him fuming with suppressed rage and determined to destroy both Cassio and Othello.
Iago's twisted jealousy expresses itself in a desire to destroy Othello's happiness with with his bride Desdemona, as well as Othello's trust in Cassio. On hearing of the marriage, Iago first tries to incite Brabantio, Desdemona's father, into thinking of it as a virtual abduction and rape by a black man of a white woman. This does not work, as Desdemona is able to convince her father that she is in love with Othello and married him freely. This leads Iago to try a new tact: insinuating to Othello, who is insecure about his age and race, that Cassio and Desdemona are having an affair right under his nose. He also gets Cassio drunk so that Othello dismisses him from his post.
Insecure, and wanting his wife to himself—being jealous of her attentions paid to any other man—Othello accepts Iago's framing of what is an innocent friendship between Cassio and Desdemona as a sordid, ugly affair. He is so jealous of this imagined affair that he ends up killing Desdemona rather than having her, as he thinks, be sexually involved with another man.
In Othello, Shakespeare shows that jealousy is a poisonous trait, a form of madness that leads people to evil acts.