What was the significance of Emily's father in her life?
For Emily, her father played a very important role. We know from the story that after her father died, she 'went out little'. She also refused to believe that he was dead, telling people who came to the door that he was not dead. Additionally, she would not allow him to be buried. The town had to come in and bury him. This shows us that she was deeply affected by his death.
He appears to have been very domineering. We have evidence of this in that he didn't think any man in town was good enough for her. So she grew older and did not marry. This shows how involved he was in her personal life.
Her father also took care of things for her providing her with a house and so forth. His legacy continued after his death; while he was living the current mayor did not make him pay taxes. After his death and a new administration tried to make Miss Emily pay taxes, she refused on the grounds of the arrangement her father had with the town while he was living.
Her father's death and her non acceptance of it foreshadows the death of the man she chose after her father's death, Homer Barron. So it is significant that she could not accept her father's death as it foreshadows her reaction to Barron's death.