Characters in a play generally function to forward the plot, explain what is going on, and illuminate the drama's themes. Emilia does all three, making her a significant character in Othello.
Shakespeare needed somebody to steal Desdemona's handkerchief so that Iago could bring his evil plot to fruition. As Iago's wife and Desdemona's attendant, Emilia is the perfect person to fulfill this task. She doesn't know why Iago wants it, but she allows him to browbeat her into doing the deed. Ironically, even though she loves Desdemona and is loyal to her, she becomes an instrument in her destruction.
Emilia also functions at the play's end to explain what has happened. As she realizes she was used as a tool by her husband and manipulated into betraying Desdemona, her integrity causes her to expose Iago's hand in the plot. He kills her, but too late—the truth is out.
Importantly, Emilia illuminates the theme of good versus evil. She is a foil or contrast to her husband. Unlike Iago, she is capable of friendship, loyalty, and love, caring deeply for Desdemona and appreciating her goodness. She is a practical, and in some ways cynical person, but at heart she is ethical. The fact that even she, Iago's wife, is deceived by him, makes it more plausible that Othello also fell for his tricks and manipulations.