"A Rose for Emily" begins with a sense of mystery. It begins with the death of our title character, Emily Grierson. In fact, the audience learns that "Miss Emily" has been a mystery to the town for the years leading up to her death. Her death gave the people in the town the chance to look into her house and look for answers to questions they've had for years.
At the beginning we learn that her house had been nice, years ago, but years of disrepair have left the house, and its inhabitant to fall apart and become an eyesore. Her taxes are also a mystery. Tax records show that in 1894 mayor, Colonel Sartoris, remitted her taxes for an unknown reason. Future mayors have trouble getting her to pay after this.
The opening gives many questions about Emily. This technique draws the reader in to continue reading to understand more bout her.