For most of "The Knight's Tale," Emily exists only as an object of desire. She's basically just a beautiful noblewoman whom Palamon and Arcite admire from afar, then fight over. Even though both knights say she's the cause of all their pain and suffering, she hardly knows who they are for most of the story.
For the first half of the story, most of what we know about Emily comes from what Palamon and Arcite say about her, which is that she possesses such "fairnesse" and "fressh beautee" that Palamon, at least, doesn't know "wher she be womman or goddesse" (243). We also have a few biographical details, like the fact that she's Theseus's sister-in-law, and was captured alongside her sister in Theseus's siege of Scythia. That's all we know about Emily for a long time.
All of that changes when Emily goes to pray at the temple of Diana on the day before Palamon and Arcite's joust. There, she washes herself, lights the ritual fires, and prays to Diana: "Chaste goddesse, wel wostow that I / Desire to ben a mayden al my lyf, / Ne nevere wold I be no love ne wyf" (1446-1448). Emily, the idealized object of Palamon and Arcite's desires, actually has no desire to marry anyone! Who would have thought? Furthermore, she tells Diana, she much prefers hunting and woodcraft to marriage and childbirth, and would like to be one of Diana's virgin huntresses forever. She concludes her prayer by asking Diana to end the fight between Palamon and Arcite by ending their burning love for her, or, if that can't be, to marry her to the one that loves her the most.
With Emily, then, we have a character who's not insensitive to the suffering of Palamon and Arcite, but who just never wants to marry. Unfortunately for her, she lives in a world in which noblewomen exist to reward worthy men. In the end, what Emily wants is just not all that important. Maybe for this reason, Diana doesn't even go to bat for Emily, telling her at the end of Emily's prayer that it's written in the stars that she must marry either Palamon or Arcite. Emily doesn't put up a fight, but you've got to wonder what she's really thinking as she watches the course of her life be decided for her.