Iago understands human nature. That's his enduring power. He works with who people are. That's what makes him such an effective manipulator: he never makes characters do anything that they are not already predisposed towards doing. His genius is in being able to predict what people will do in different situations, and to use those behaviours to his advantage. Although Iago robs Roderigo blind, Roderigo gives nothing to Iago that he was not already willing to give for the hope of attaining Desdemona. Roderigo's fault is in thinking Desdemona can be bought. Iago uses it. Similarily, though he exploits Cassio's flaws (his intemperance with alcohol and women) Cassio does nothing that he is not already presdiposed to doing. Cassio is predictably violent when drinking and reticent about acknowledging his affair with a prostitute. Othello's weakness, his pride and certainty, also predispose him towards the actions that follow.
Each of these characters falls victim to his own weak character: they are all destroyed by vice. From a moral perspective, we might even say that they get what they deserve. What is most brilliantly evil about Iago, however, is his ability to use virtue to his advantage. Desdemona's virtue is as predictable as the others' vice. Iago's ability to manipulate her virtue and to use it against her shows he is a true master of human nature.He could use his power for good, but unstead he destroys them all.
It is also important to address the structure of the play in answering this question. Iago's soliloquys shape the entire play. If not for his soliloquys, we would not understand how his scheme is planned, how he contradicts himself each time he reveals his motives, why his ego is hurt at points during the play, and i the end, each soliloquy adeptly forwards the plot. For the audience, without the knowledge of Iago's plans, we would not entirely understand his power over Othello, or for that matter, any character in the play. The structure of the play, therefore, mirrors Iago's control.
You might think of Iago as a sort of puppet master, one who works behind the scenes, unseen, and pulling the strings. Envious of higher positions in Othello's army (he's an ensign), outwardly he is "a man...of honesty and trust" but actually he is a villain without a conscience; a "viper" and an "inhuman dog."
His dual nature is first realized in Act One, when Iago's first plot against Othello is to tell her father about his daughter's elopment with the nobleman. He brings another puppet onstage, Roderigo, to take the fall.
Often, Iago (and the play) is helped along with his wicked schemes by fortunate circumstance. For example, Othello chooses Iago to accompany Desdemona; therefore, Iago has the opportunity to observe her with Rodergio and come up with the material needed to construct a story of infidelity. Additionally, along the "luck" theory, Iago comes upon Desdemona's handkerchief, which he uses against her as "evidence."
The play ends with Iago's punishment, his letters of betrayal found in the coat pockets of the slain Rodgerio. Iago stays a force in the play until the very last lines, when "the Spartan dog" is hauled off on Cassio's orders. He will be tortured and murdered for his crimes.