Describe your management style.
Since it's likely you will be managing teams of people in this role, the interviewer wants to learn about your management style. There are multiple styles out there, including authoritarian, visionary, democratic, and laissez-faire, among others, so be honest and discuss your preferences and methods. This will help both you and the interviewer to determine if you will be a good fit for the role or not.
"At this point in my career, I have worked under several different managers, and I've found that everyone is different. There are pros and cons to each management style; however, when I myself am put in charge of others I prefer to use a democratic management style. I choose to manage in this way because I value the feedback, thoughts, and ideas of the people I'm working with, no matter their rank or seniority, and I encourage idea sharing and employee participation. Ultimately, as the manager, I retain the final decision-making authority, but I first take into account the thoughts of those around me. I also believe in clearly communicating expectations, providing deadlines, and then giving people the space and time they need to get the job done of their own accord. I trust in their intelligence and experience and don't feel the need to micromanage them."