In "A Rose for Emily," Emily is a complex character, and we can discern several of her important characteristics from Faulkner's descriptions.
One of the first things we learn about Emily is that she is stubborn. After her father dies, town authorities approach her to try to persuade her to pay taxes. However, no matter how much they insist, she refuses, claiming that a former mayor of the town has exempted her from taxation.
Emily is insecure and reclusive. After her father dies, she retreats into her house and stays there, except for a brief interlude during which she goes for buggy rides with Homer Barron. After she kills Barron, she remains in the house for the rest of her life.
Emily is mentally unstable. We see this first when she initially refuses to give up her father's body after he dies. This becomes even more obvious when we learn that she has killed Barron, presumably because he was going to break up with her and move away.
Emily is murderous. Most women, of course, would be sad and depressed if their boyfriend announced his intention to leave. However, they would not resort to killing him and then sleeping with his dead body.
Finally, Emily is proud and duplicitous. She covers up the murder she has committed with an attitude of haughtiness.