Why does Othello become angry at Desdemona in Shakespeare's play Othello? Who are Iago and Cassio?

Othello was angry at Desdemona because he believed that she was cheating on him by having an affair. He had been manipulated into believing a lie. Othello had fallen in love with her when she asked him to repeat, to her only, the dramatic stories of his past that he had been telling her father, Brabantio, on his numerous visits to their house.

Desdemona eavesdropped on Othello's conversations with her father and was enthralled by his tales. She fell in love with his stories and, consequently, with him. Othello was impressed by her deep interest and her empathy and, likewise, fell in love with her, as he states in the following extract from Act 1, Scene 3: 

She loved me for the dangers I had pass'd,
And I loved her that she did pity them.

The two lovers decided to elope since there seemed little chance that Desdemona's father would agree to their marriage, since Othello was a foreigner and much older than her young and beautiful self.

Iago was Othello's ancient in the Venetian army, which meant that he was not much more than a messenger or manservant. Iago sought promotion to be Othello's lieutenant, which meant that he would be the general's second in command. His request was turned down even after three senators had approached Othello and made an appeal on his behalf.  

Othello appointed another person, which infuriated Iago. He was bitter and resentful and used Othello's snub as a reason to seek revenge against him. At the beginning of the play, he told his friend, Roderigo, that he would appear to remain loyal to the general to win his trust just so that he could avenge himself. He told Roderigo in Act 1, Scene 1:

I follow him to serve my turn upon him.

Iago manipulated and mislead Othello to such an extent that he believed his wife was having an affair. Othello's jealousy eventually drove him over the edge and he murdered Desdemona in their bed by smothering her. When he later discovered that he had made a foolish mistake, he took his own life.

Cassio was a young and handsome Florentine soldier who Othello appointed as his lieutenant. Iago was extremely resentful of him since he believed that Cassio had no experience and was more of a mathematician than a soldier, whilst he, Iago, was battle-hardened and experienced. He had been loyal to Othello and had been at his side in many a battle. Furthermore, Cassio was an outsider, which, as far as Iago was concerned, added insult to injury. His hatred for Cassio was so deep that he promised to also take revenge against him.

Cassio was the one Iago told Othello Desdemona was having an affair with. It was easy to convince him because Cassio was good-looking and something of a ladies' man, whilst Othello was practically middle-aged and dark-skinned. Iago played on his insecurities in this regard. Cassio was discharged from duty by the general because of Iago and Roderigo's manipulation, which compromised his position. He was later advised by Iago to seek Desdemona's help in asking Othello for his reinstatement.

Cassio became ensnared in Iago's web of lies and deceit and Othello soon made a pact with Iago to have him killed, too. Fortunately, Iago's attempt to execute him failed. In the end, Cassio was given the deceased Othello's title and Iago was removed and incarcerated to face torture and further sanction.