It's a two-way street. Yes, you're there to sell yourself, but they're selling the job, too.

The answer will help you define "the organization's strengths and weaknesses with this insider's perspective," says Michael Erwin, a senior career adviser at CareerBuilder.

If this person would be your boss, and you feel at ease, you might ask: What's your management style? What challenges make you excited to come to work each day? What do you like the most about working here? These kinds of questions let somebody see that you're genuinely attracted to the job and can help you determine whether the company is a good fit for you.