How does the storm that destroys the Turkish fleet symbolise ambition and concern for one's reputation for the main characters in "Othello"?
The storm symbolizes the end of the peaceful first part of the play and marks the beginning of Iago's troublemaking. Othello's concern for reputation becomes obvious after the storm when he makes Cassio his first leutenent over Iago because Cassio is courtly and well mannered and everything that Othello feels a Venetian should be (and worries that he is not himself).
Since Othello is already concerned about his reputation and is already worried about how he is perceived in Venetian society (since he is a Black man, or a "Moor"), it makes it very easy for Iago to start plotting against him as he already feels spurred by not being chosen for the promotion, he immediately starts plotting against Cassio (who took Iago's "rightful" place) and secondarily to hurt Othello where it hurts most - by starting malicious gossip about his wife who he is desperately in love with. Additionally, since Iago has massive issues with women, he also suspects that Othello is having an affair with his wife (which hurts his pride further), though that's not at all the case.
Cassio's feelings towards Desdemona are admiring, though strictly platonic. It is however in this scene where Iago starts to cast doubt into Othello's mind about Desdemona's fidelity.