How to answer "Tell me a time when you failed" in a job interview

One of the interesting questions I come across nowadays when making job applications is a "Tell me a time when you failed. Explain the situation and what you learned from it." First time I saw this question, I was taken aback and wondered why anyone would ask me that. Why does what happen in the past matter? Then I was confused. What situation should I talk about? Should I talk about the time an event did not succeed due to disorganization? Should I talk about the time I ordered the wrong coffee for my boss or that I got fired? I had so many questions running on my mind, and yet I was on a timer. I had to finish the 4-page questionnaire in 20 Minutes. I finished all the other questions and went back to this one. I was almost out of time, so I noted down the first answer that came to my head. That question might have cost me the opportunity.

I've asked a couple of people about that question, and they have different answers. Some say you should completely honest, lay yourself bare, that employers like people who are not afraid to admit their faults and accept that they've learned from the experience and are better people. On the other hand, others have said don't tell the employer what they don't need to know. Pick a soft situation that shows failure but don't put yourself out there too much. In the real sense, it's very difficult to know what an employer is looking for in this question, and job applicants are caught between a rock and a hard place trying to answer that question.