Why are Emilia and Bianca so important in the play Othello?
In additions to the points mstultz72 has made, it is important to consider their functions in the plot or story of the play.
Both do contrast with Desdemona: Emilia's less than ideal relationship with her husband, Iago, contrasts strongly with the deep passion between Othello and Desdemona; while Bianca is spoken about by Cassio as a mere plaything and certainly not wife material in any sense.
But they also serve the plot of the play as characters in their own rights, especially as concerns the event surrounding the handkerchief.
Emilia finds the handkerchief that Desdemona drops and, instead of returning it to her mistress, she gives it to Iago. She then lies to Desdemona, claiming she doesn't know where it is. This one action sets into motion the escalation of Othello's jealousy and the supposed proof that Desdemona has been unfaithful with Cassio.
This "proof" comes from Bianca. Iago has given the handkerchief to Cassio, who gives it to Bianca. It is a pivotal turning point in Othello's jealousy when Bianca (while Othello watches in hiding) returns the handkerchief to Cassio. What should Othello think now? Clearly, Desdemona has lied about "having" the handkerchief and has given it to Cassio??!!
This sequence of events surrounding the whereabouts of the handkerchief are key to the development of Othello's "evidence" against Desdemona, and Emilia and Bianca are key players in these events.
In Othello, Bianca and Emilia serve as foils for Desdemona. Taken together, Shakespeare portrays the three social classes of women: upper-class (Desdemona), middle-class (Emilia), and low-class (Bianca). Whereas Desdemona is a silent, submissive wife, Bianca and Emilia are more worldly, practical, and outspoken in their critiques of men.
What's more, these two women are key in the jealousy scheme that Iago wages against Othello, as they both have their hands on the handkerchief. First, Emilia steals it for her husband; then, Iago gives it to Cassio, knowing he will give it to Bianca. When Othello sees it in her hands, he becomes enraged and vows to kill Desdemona and Cassio.
The women are all victims of misogyny in the play. Ironically, Bianca, a prostitute, will be the only survivor. Emilia will be killed by her husband for essentially talking too much.