Desdemona intervenes on Cassio's behalf because she knows he is a true friend to her and Othello, as well as a loyal soldier to his general. Cassio played an important role in her and Othello's relationship and ultimate marriage.

Cassio believed in Desdemona's love for Othello and that Othello would be a good husband to her. Cassio played an intermediary role in helping smooth the way with her father.

Although Cassio lost his job after just one episode of drinking, Desdemona knows that Othello will resist changing his mind. One reason is that as a military commander, he is used to making decisions quickly and sticking to them. Changing his mind could undermine his authority and make him seem weak. Othello also has high standards and is unforgiving of others' foibles.

Iago has convinced Cassio to appeal to Desdemona to intervene on his behalf with Othello. Cassio was fired because of his behavior (Iago gets him drunk, and then Cassio reacts violently when he is insulted). Othello fires Cassio, who feels terrible about what has happened.  Cassio is friendly with Desdemona, and Iago convinces Cassio that he should ask Desdemona to ask Othello, who is after all her husband, to reinstate Cassio.  Desdemona seems to ask this favor of Othello in a sort of "if you love me you will do this" sort of way.  Othello's reluctance irritates her, and she keeps asking him to reinstate Cassio. For the play's plot, Desdemona has to take Cassio's part with passion, because Iago uses her defense of Cassio to frame them in their "affair."