By approaching this question with openness and honesty, you can show the interviewer that you are not afraid to face up to your past mistakes or failures. The failure you choose needs to somehow relate to the position you are applying for. Identify a quality or skill you need in the job you want and think of a past experience where you made a mistake in this area. Discuss a specific example of a time you made a mistake and briefly explain what the mistake was, but don't dwell on it. Quickly switch over to what you learned or how you improved, after making that mistake. Finally, remember that you are trying to get hired and your answer needs to show you as an adaptable and willing employee, not a liability.

"I was so determined to show that I was a team player at my first job that I never said no to a task. Eventually, that led to me becoming so bogged down that I was staying late but still not managing to give my projects the attention they deserved. As a result, the first major presentation that I gave was a flop. It was very disorganized, and I was unable to articulate what I meant. After that experience, I learned to manage my time more effectively and only take on what I knew I had time for so that I could do my best. My presentation skills grew stronger, and I received departmental recognition for the deals I was able to facilitate with clients thanks to my attention to detail."