Once you have understood how to use the plot and the characters, you should move onto the themes. The themes are the basic ideas in Othello - we have already met one - the play deals with the subject of jealousy and revenge. There are others, such as race and foreign cultures or appearance and reality.
Perhaps the most obvious subject or theme in Othello is revenge and jealousy. Iago is the key to almost everything that happens. He has been passed over for promotion, so he dislikes Othello and must be jealous of Cassio. He thinks Othello might also have slept with his wife. However, we can never be completely sure what motivates Iago to be so destructive - he manages to get Cassio dismissed but then Iago doesn't seem interested in Cassio's job, only in causing more problems. We also learn that Iago has tried many times in the past to steal the handkerchief that means so much to Othello. This tells us that he was planning against Othello long before his promotion was blocked.
Jealousy affects most other characters as well. Othello cannot bear the fact that his wife might be having an affair and Iago cleverly plays on this. For instance, when Othello thinks his wife is honest and needs proof of the affair, Iago asks if he would want to see her 'topped' (i.e. with a man on top of her) but then tells Othello to calm down and that his mind 'perhaps may change'. Of course it won't - Iago presents the worst image possible to Othello knowing the damage it will cause.
Jealousy affects almost all of us at sometime in our lives, and Shakespeare shows the destructive effects it has throughout the play. In fact only two characters seem unaffected by jealousy - Desdemona and Cassio. Desdemona dies, but everyone realises what a good woman she was, and Cassio is rewarded by taking Othello's place as general (and by deciding Iago's punishment).