What are some of your key values which contribute to your performance as a senior staff engineer?

An interviewer will ask you about your professional values for two reasons. One is to determine that you have established core values and use them to direct your professional activities. The second is to determine if your values align with those of the organization. By the time you have been invited to an interview, the hiring manager has already determined that you have the skills and experience needed for the job. The purpose of the interview is to confirm their assessment and determine if you would be a good fit for their organization. Questions about values address this latter point.