What quality would bring to this role that other candidates may not have?
I've seen hiring managers ask questions like this to give the candidate the chance to distinguish and sell themselves as the best candidate for the job. If your interviewer at the USPS asks this, they want to hear you talk about a quality or skill you possess that hasn't been discussed and can't be found on your resume.
"I have a unique ability to strike up a conversation and build rapport with nearly anyone very quickly. This skill is beneficial in customer service, and I feel I would be very warm to the customers I serve in the post office every day."
There are some things that your resume cannot do, and showing off your fabulous personality is one of them! Talk to the interviewer about one of your unique qualities, and explain how it will benefit the USPS. No matter what you choose to discuss, make sure it is a memorable quality that your interviewer will remember in the days following your interview.
"I didn't include my training and experience in auto mechanics on my resume. As a rural carrier with the USPS, I know these skills would be helpful should I ever experience troubles on the road."
