From the commencement of the play, Othello is full of ironies, most of which are or become obvious to the audience through Iago's character.
"Honest, honest Iago," the least honest of all, steers the plot and is so manipulative that, as circumstances permit, he is able to confuse, convince and connive to the point of bringing out the worst in otherwise honorable characters.
The audience is not kept waiting long before Iago hints at his personality and warns - "I am not what I am" (I.i.65). The irony surrounding this comment is so intense as it is almost as if he is practising reverse psychology - after all he warned the audience right here at the beginning. Despite this, no one would expect such skill in maneuvering people to commit the most heinous deeds possibly because as Othello himself repeats many times "Iago is most honest" (II.iii.7)
As most of the irony in Othello surrounds Iago, this supports the theme of appearance versus reality. Such is Othello's trust of Iago that he entrusts Desdemona to him. This act is however contradictory as, if he trusts Iago so fully and completely, why did he not make him his lieutenant?
A man he is of honesty and trust. / To his conveyance I assign my wife" (I.iii.284-285).
This makes the circumstances doubly ironic as the plot of Othello could have been so different had Othello not angered Iago and, subsequently, without Iago's need to avenge himself and restore his (non-existent) honor and reputation, there would have been little or no story!
Iago insists that reputation is laughable and tells Cassio so:
Reputation is an idle and most false imposition (II.iii.259)
but it is his feelings of rejection by Othello and the apparent tarnishing of his reputation that drives him. He is trying to convince himself as well as anyone else which in fact makes his whole character an ironic one. It is his own needs and his ability to manipulate situations that allow him to capitalize on the importance of reputation to any of the characters in Othello.