1. One of my favorite lines has to do with the irony of Iago in this play. He appears to be a close confidante of Othello. However, in reality he is a back-stabbing double-crosser who is setting Othello up to believe that Cassio is in a relationship with Desdemona. In fact, in the middle of one of his attempts to look trustworthy, Iago himself says this:
Men should be what they seem;
Or those that be not, would they might seem none!
(Act III, scene iii)
How ironic that Iago would say this of Cassio who needs not pay attention to this thought since he already obeys it. It actually needs to be employed by Iago who is very far from what he seems.
2. It appears as if Cassio and Desdemona are in a relationship, as was alluded to earlier. This discussion and suspicion goes on for the majority of Acts III and IV as Iago convinces Othello first that Cassio has affection for Desdemona, then that he looks at her a certain way, that he "lies" with her in his chamber, and eventually that the discovery of the handkerchief in his chamber must mean something. Iago relies on Othello's dependence on appearances. Even though reality is different, Othello comes to believe in the appearances because of the way Iago stages everything.
3. It appears to Bianca that Cassio has a new mistress. This discussion in Act III, scene iv demonstrates the discovery of a handkerchief that was actually planted in Cassio's chamber. He plays it off as if it is from an old girlfriend, when in fact he does not realize that it is the handkerchief that Othello had given to Desdemona.
BIANCA:O Cassio, whence came this?
This is some token from a newer friend.
To the felt absence now I feel a cause:
Is't come to this? Well, well. (195)
CASSIO:Go to, woman!
Throw your vile guesses in the devil's teeth,
From whence you have them. You are jealous now
That this is from some mistress, some remembrance:
No, by my faith, Bianca.(200)
BIANCA:Why, whose is it?
CASSIO:I know not, sweet. I found it in my chamber.
I like the work well. Ere it be demanded—
As like enough it will— I'ld have it copied:
Take it, and do't; and leave me for this time.(205)
This discussion demonstrates that an item can make a sitaution appear different from reality.
This question has been answered time and time again on eNotes. Here is a comprehensive link for you: http://www.enotes.com/othello/search?q=appearance+vs.+reality