When devils with the blackest sins put on
They do at first with heavenly shows,
as I do now.
In his soliloquy Iago explains why he is giving Cassio advice. After getting him drunk, getting Roderigo to provoke him in a fight, and telling the story to Othello so that Othello has no other recourse but to fire Cassio, Iago tells Cassio to go to Desdemona and ask her to help him restore his position and good favor with Othello. Of course, this is excellent advice on the surface. If Cassio is too embarrassed to speak to Othello, Desdemona who is kind and compassionate would be an easier audience. And, she is in a position to influence Othello's thinking.
Cassio recognizes the wisdom of this advice as well. However, these "heavenly shows" are really the devil's workings, for Iago is going to to make it seem that Cassio's talking with Desdemona is not innocent, that the two are involved with each other.
This speech I think is the key to understanding Iago's method of acting. He seems wise, loyal, and caring. He puts on "heavenly shows," but in reality he is the "devil" with the "darkest sins." The key problem in the play is the fact that the characters misjudge Iago, thinking him virtuous when he is actually quite demonic.