I feel like that in the first three “Halo” games Cortana’s character wasn’t developed. That she was a placeholder of a character — a blank slate that the player filled in themselves.
Cortana was developed more in books, but since different writers would be writing different stories her character never seemed consistent. In one story (“Palace Hotel” by Robert McLees) Cortana would be cold, albeit sarcastic, willing to do whatever it took to complete a mission. While in another story (“Human Weakness” by Karen Traviss) Cortana would feel regret, she would feel vulnerable — she would not be the same person she had been in “Palace Hotel.”
In Halo 4 Cortana is like an actual person — someone with desires, fears, goals — and not only someone who tells the player where to go, like a GPS.
The word I would use to describe Cortana would be “Mysterious.”
There’s just something about Cortana that I can’t put into words: A goodness, truth, and beauty that is present in her body — reminiscent of Eve’s original purity in the Garden of Eden — and in her character itself. Cortana is strong, but she’s not afraid to be “weak.” (i.e., Cortana is not afraid to express her insecurities.)
Cortana is naked, physically and emotionally, but there is still a mystery about her. Her nakedness doesn’t take away from her mystery — it adds to it.
UPDATE: January 23rd, 2015:
The mystery about Cortana has to do with her femininity — that she identifies as a woman.
Women are beautiful and mysterious. I mean “beautiful” in this way: You (a woman) and I (a man) are both human beings, and yet there is not just a physical difference between us, but a mental, emotional and, I would say, spiritual difference as well. Being a man, I will never be able to see the world exactly as you do, and it is that difference in how you see the world that is mysterious and, thus, beautiful.