Typical interview questions often take the form of 'imagine the following hypothetical situation X. what would you do?' Candidates tell people what they want to hear, and all the question does is establish that the candidate knows what the interviewer wants to hear. Psychology research shows us that people assign themselves better positive traits than their behavior would indicate.

Behavioural interview questions have the interviewer ask a question of the form 'Tell me about a time when X happened, and what you did.' By asking for a personal anecdote, people are less likely to bring that positive trait assumption with them to the interview, and interviewers get a more honest appraisal of future behavior.

Of course, psychology also fundamental overattribution bias, which says we attribute behavior far too much to the person than the situation. For example, somewhere in this thread is an interview question asking about doing something for the customer that wasn't planned, and that the interviewee worked in hardware design, where unplanned features results in unplanned testing, unplanned Bill of Materials and ultimately an unplanned cost to your customer. When we learn that the candidate never did anything unplanned, we learn more about the situation -- customers bear all costs of design and production -- than the candidate.

I would define it as a question about how you handled a particular type of situation or how you would handle a particular situation.

I think it's primarily used in contrast to a coding question.