Ask HN: Can you explain how a database index works in an interview?

Over the course of the past year or so I've been doing a fair number of interviews for web developers (full-stack and back-end) and have asked this question nearly every time. Across a wide range of experience levels, not one has been able to answer this question well. About half just honestly say they can't, a quarter know a little bit, but can't explain it well, and the other quarter come up with some wild response. It is not my intent for this to be a "gotcha" question, I ask because I was once asked it and the learning I did after that interview really stuck with me.

How would you explain how an index works?