The most significant use of animal imagery is in Act I, scene i, and it is used in reference to Othello.
Iago and Roderigo are under Brabantio's window, awakening him to alert him to the fact that his daughter, Desdemona, has run off with Othello. Under cover of darkness, Iago says:
Even now, very now, an old black ram
Is tupping your white ewe. . .
. . .you'll have your daughter cover'd with a Barbary horse; you'll have your nephews neigh to you. . .[Y]our daughter and the Moor are now making the beast with two backs.
All of these derogatory images are meant to anger Brabantio, as Iago and Roderigo refer to Othello having sex with Desdemona in an animalistic way. Throughout this scene, it should be noted, Othello is only ever referred to as the "Moor" or by racial slurs like "thicklips." All of this is intended to add up to an expectation of who/what Othello is when the audience meets him in Act I, scene ii. How surprised they are to see a dignified, noble and beautifully well-spoken man arrive onstage, overturning the expectations created by the opening scene..
So, the animal imagery aimed at Othello in Act I, scene i is meant to prepare a false perception of him in the mind of the audience, while also highlighting the prejudiced points of view of Iago, Roderigo and Brabantio.
Animal imagery is used throughout the play. It is first used by Iago. He references other characters with this imagery. He calls Othello "a black ram" and an "ass." He calls Desdemona a "white ewe," Roderigo, "a snipe." This imagery shows Iago's sense of superiority over others in his life. He knows he can control each of these characters.
What is interesting, though, is that as characters come under Iago's influence, they also begin to use animal imagery. In Act 2 Roderigo calls himself a "hound," and Cassio refers to himself as "bestial." In Act 3, Othello begins to use animal allusions to describe his relationship with Desdemona: "I'd rather be a toad . . ."
When characters begin to disengage from Iago's web, they begin to use animal imagery against him, calling Iago what he is. Roderigo is first calling Iago a "damned inhuman dog." Other characters follow suit.
Examining the animal imagery in the play is a good way of exploring Iago's manipulation and his power over the other characters.