At this point in the play, Brabantio has had to accept that Othello did not use witchcraft or sorcery to win the heart of his daughter, and he has had to accept also that there is nothing he can do about the fact that his daughter Desdemona has married Othello. In the given quotation, Brabantio is warning Othello that Desdemona will deceive him, her husband, just as she has deceived her father. Brabantio is telling Othello that he should keep a careful eye on his new wife.

When he says, "Look to her," Brabantio means that Othello should always carefully watch Desdemona. He is implying that Othello should expect Desdemona to betray him, as she has betrayed her father. It is also important that, in this quotation, Brabantio reminds Othello that he is a "Moor." This reminds Othello that he is a black man and, at least originally, a Muslim, in a white, Christian Venice. In other words, Brabantio is here reminding Othello that in terms of his color and his religion, he is unworthy of Desdemona. This is a persistent idea that Iago also later manipulates to convince Othello that Desdemona's love for him is only a fleeting fancy.

Brabantio then says to Othello, "if thou hast eyes to see." The implication here is that Othello is perhaps not perceptive enough to see Desdemona for who she really is. Upon hearing this Othello may question, albeit only momentarily, whether Desdemona is really as perfect and as angelic as he thinks she is. Othello may also question whether he is perceptive enough. It is also important that the quotation is formed as a rhyming couplet. This makes the sentiment expressed more emphatic and more memorable.

Brabantio's lines here are significant because this is the first time Othello is made to doubt Desdemona's character. Brabantio is bitter about Desdemona's deception of him and Othello's marrying his daughter without his blessing (which he never would have given since Othello is a Moor) so he is trying to make their marriage begin on shaking ground by pointing out to Othello that Desdemona does have the capability to be unfaithful to some degree.

These lines haunt Othello later in the play as Iago starts making the case that Desdemona is violating her marriage vows. While Brabantio's words are the product of anger and perhaps even hurt, Othello does not consider this. He begins to view them in a prophetic light. Desdemona's willingness to break social mores (unquestioning obedience to the father) to be with the man she loves ends up becoming a weapon against her: instead of proving that she loves Othello more than anyone else, her actions instead paint her as wayward and duplicitous to the very man she gave up her family for in the first place.

This is a significant quote from Othello because it signifies the first seed of doubt that Othello experiences in the play. Othello’s tragic flaw as the hero of the story revolves around his pride and his worry that Desdemona is unfaithful to him. When she betrays her father’s wishes in secretly marrying Othello—something Barbantio sees as a great insult and the possible result of black magic. Barbantio is, in essence, telling Othello—if Desdemona can betray me like this, she can do the same to you.

The doubt that Barbantio plants in the first act blossoms into the eventual murder of Desdemona by the end of the play. It is Iago, the main villain of the play, who uses what Barbantio says to create the doubt in Othello’s mind throughout the play. Eventually, the idea that Desdemona cannot be trusted comes to full fruition in Othello’s mind, and he murders her for the sake of his own pride and jealousy. Barbantio’s words had their effect on Othello, even though Desdemona is innocent of any guilt in the entire tragedy.

In Act One, Scene Three, Brabantio warns Othello about his daughter's capacity for dissembling by saying:

Look to her, Moor, if thou hast eyes to see. She has deceived her father, and may thee. (Shakespeare, 1.3.288-289)

At this point in the play, Brabantio has recently discovered his daughter's relationship with Othello and initially accuses him of using black magic to win Desdemona's heart. Being that Othello is a dark-skinned Moor, who is an outsider and much older than Desdemona, Brabantio had no concern that his daughter would ever consider being with Othello. After Roderigo and Iago inform him that Othello has secretly married her, Brabantio launches into a tirade and seeks justice from the Duke. However, Othello eloquently describes how he won Desdemona's heart and the Duke dismisses Brabantio's argument.

Brabantio's warning about Desdemona's dishonesty and guile will plague Othello later in the play. In Act Three, Scene Three, Iago suggests Desdemona's infidelity and recalls her cunning nature by telling Othello:

She did deceive her father, marrying you, And when she seemed to shake and fear your looks, She loved them most. (Shakespeare, 3.3.211-212)

Othello will recall Brabantio's warning, which appears to be prophetic in his eyes and is further evidence that Desdemona is dishonest.

One of the major problems in the case of Brabantio, if we look at this line from his perspective, is that he was not aware of the love affair blooming between Desdemona and Othello.  He thought a great deal of Othello as a general and as a man of interest, but never once thought his daughter, the child of nobility, would sink to follow after a Moor, acceptable as a general but not as a son in law.

For Othello it suggests that he might not be capable of seeing the type of guile that Desdemona demonstrated in hiding this from her father.  It addresses perhaps as well his own lack of confidence in anything not related directly to war.