Othello, a Moor, comes from a different country than the Venetian Desdemona, is much older, has had a very different set of experiences, and is black in a culture that views his race with disdain.
Desdemona gets to know and fall in love with Othello largely through the exciting stories he tells about his exploits as a soldier. Othello gets to know Desdemona largely through her empathy ("pity") with his tales. Othello states in the first act:
She lov'd me for the dangers I had pass'd,
And I lov'd her that she did pity them.
Desdemona has to trust that Othello's stories about himself are true, that he is the man he represents himself to be. Othello has the harder job: he has to have faith that a beautiful young woman from a different culture who could choose from many suitors would genuinely love a middle-aged black soldier like him.
Iago plays primarily on the insecurities that hover in the back of the mind of the middle-aged Othello. Othello fears he is not worthy of his young wife's love, and he worries that her love is merely a passing infatuation. Iago does have to plot and plan to cause Othello to kill Desdemona, but it doesn't take all that much to grow the seeds of doubt in his mind. It is plausible to Othello that Desdemona would lose interest in him and move on to Cassio.
Iago fully exploits Othello's trust in him as a faithful fellow solider. Iago is also able to undermine Othello's faith in Desdemona by playing on stereotypes of Venetian women as unfaithful.
Othello and Desdemona need to have faith in each other's strength of character and sincerity for the relationship to work, but unfortunately, Othello temporarily becomes prey, through Iago's manipulations, to the worst impulses brought on by his doubts and insecurities.
Desdemona shows great faith in Othello by the simple fact that she, a white noblewoman, was willing to elope with an exotic dark-skinned Moor. She risked her family's wrath and her own reputation in doing so.
Othello and Desdemona enjoy a wonderful, passionate love that seems above reproach. Their marriage has been accepted and Othello is honored as an excellent soldier.
Ironically, Iago points out to Othello that Desdemona deceived her own father in order to run away with Othello, chipping away at Othello's faith in his wife. Iago is able to use subtle manipulation, persisting until he convinces Othello that Desdemona has been unfaithful to him.