At this point in the play, Iago and Roderigo are outside Brabantio''s house, shouting up to him about his daughter, Desdemona. They tell him that his daughter, a white woman, has eloped with Othello, a black man. This play was first performed in 1604, and at this time the prospect of a white aristocratic woman marrying a black man would have been scandalous.
When Iago shouts to Brabantio that his daughter and Othello are "making the beast with two backs," he is crudely implying that Othello and Desdemona are, at this very moment, having sex. If the thought of a white aristocratic woman marrying a black man would have been scandalous at this time, then the prospect of that woman having sex with a black man would have been even more outrageous, especially from the perspective of that woman's father.
The image of a "beast with two backs" suggests two people engaged in sexual intercourse because, during intercourse, all that might be seen of those two people would be their backs. The word "beast" also connotes the animalistic, primal act of sexual intercourse, while also playing up to the contemporary racial stereotype of black men as animalistic rather than civilized. Iago hopes to inflame Brabantio's anger by reminding him that his daughter is currently with a man who is bestial and brutish. In the same scene, Iago also refers to Othello as a "Barbary horse" and "an old black ram."
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