What is the role and purpose of women in Shakespeare's Othello?
From a scholarly point of view (as the asker is an educator), this is a fairly complex question, because purpose depends on the agency. That is, a purpose is not something existing "out there" but implies a purposive agent.
In terms of Shakespeare's purpose for writing the female characters into the play, we don't have any letters, diaries, or essays by Shakespeare himself explaining his reasons for writing in Desdemona and Emilia, although without the former, there would be no play, as the plot revolves around Othello's relationship with her. Also, most repertory companies of the period had male actors who specialized in female roles, and audiences appreciated their virtuosity, and so there are good reasons, in terms of the dynamics of a repertory company and audience appeal, for Shakespeare to have included these characters in the play. However, there are, as Wimsatt and Beardsley argued, limits to intentionalist criticism.
In terms of roles, this is a story of sexual desire and jealousy inflaming passions and causing the downfall of Othello, an otherwise brilliant general and honorable man. He makes a great contrast to Iago, whose fall into infamy is motivated by careerism and envy rather than a grand passion. Emilia, as well as her role in furthering the plot, acts as a foil to Desdemona. Although they are both loyal to their husbands, Desdemona acts in a morally good fashion and is a model wife, while Emilia, although not an evil character, is far weaker, and in certain ways, like Othello, led by love into moral faults. If one looks at the two couples in the play, one finds an interesting balance of love in the correct degree (Desdemona) which is purified by strong individual will and moral judgment, excessive love leading to moral lapses (Othello, Emilia) and deficiency of both love and morals (Iago). This makes for a certain structural symmetry in the play.