I learned of behavior based interviewing about 10 years ago. The goal of this type of interview is to learn how the candidate behaves in situations that they are likely to encounter in a professional environment. Most questions begin with "tell me about a situation you were in when..." The interviewer is not looking for a "best answer" but rather trying to understand what the interviewee learned from the situation - even if the experience was not positive/successful.
A successful strategy to structure your reply to these types of questions is using the S.T.A.R. approach. Your answer should be focused on the the Situation you were in, what your Task/s were, the course of Action you took and the Result. Again, even if the result was not ideal you can explain how you learned from it.
Practicing the S.T.A.R approach with someone before you go to an interview is extremely beneficial. Just like the interviewer is not looking for a specific answer, you should not be trying to come up with a specific response. The purpose of practicing is to help you to discover "your" answer so it flows naturally from you during the interview.