Iago taunts Othello throughout this scene. Firstly he implies through repeating his master's words that all is not as it seems with Cassio. He then goes on to warn Othello, in an act of dramatic irony, to counsel his own thoughts:
O, beware, my lord, of jealousy! It is the green-eyed monster, which doth mock The meat it feeds on. That cuckold lives in bliss Who, certain of his fate, loves not his wronger; But O, what damned minutes tells he o'er Who dotes, yet doubts, suspects, yet strongly loves!
We as an audience can see that Othello is already unsettled by this idea. Iago then goes further, confessing to Othello that he witnessed a dream of Cassio's which implicated him in a relationship with Desdemona:
In sleep I heard him say, “Sweet Desdemona,
Let us be wary, let us hide our loves”;
Othello is wracked to torment, and demands that Iago has real proof. As we know he has planted Desdemona's handkerchief in Cassio's chamber, we see Iago use his ultimate weapon--a form of 'proof' that will drive Othello to kill--
I know not that; but such a handkerchief—
I am sure it was your wife's—did I today(485)
See Cassio wipe his beard with.
The significance of the handkerchief--ironically the most flimsy of evidence--is as Othello's first gift to Desdemona. Iago has, at this point, succeeded in convincing Othello of his wife's infidelity.