Alternative and related questions:
Can you tell me about a time when you have failed to achieve a goal?
How do you handle being criticised?
The meaning behind the question:
There are really three different questions here but they're all very closely related. The interviewer is trying to assess how you deal with adversity – whether that adversity be in the form of rejection, failure or some other disappointment. It's also a question which gives them a useful opportunity to potentially pinpoint a particular occasion when you experienced such adversity.
Naturally, assessing how someone handles adversity says a lot about them a person. The interviewer won’t want to hire someone who can't handle it when the going gets tough.
Your answer:
When the going gets tough, the tough get going!
Rejection, disappointment, failure – everyone experiences these from time to time during the course of their careers, even renowned business superstars like Richard Branson. But one trait which sets people like Richard Branson apart from some others is that, when they do get knocked down, they always get back up again. Not only that but when they get back up, they become stronger, having learned as much from the experience as they can.
This is what you need to aim to communicate to the interviewer in your answer. Try to avoid giving a specific example unless they force you to. Just concentrate on speaking in general terms about you handle adversity. Take what could potentially be a negative topic and turn it round so that it becomes a positive selling point. Show them how you can benefit from adversity.
Example:
I'm certainly realistic enough to appreciate that things don't always go the way one would hope or expect them to go and that the occasional disappointment is a fact of life. But I feel that what's most important is how one handles such circumstances. I endeavour to learn as much as I can from any possible failures; they really are excellent learning opportunities and they can be a blessing in disguise in that sense. And it's always important to focus on the future rather than dwell on the past. If at first you don't succeed, try, try again!
Word of warning:
Even if you don't give the interviewer a specific example, you will of course have to be prepared for the possibility that they will push to get one out of you. If you do have to cite a real-life event then try to pick something which isn't too negative, try to pick something which is reasonably far back in your past and, most importantly, try to pick something where the blame, if any, wasn't solely attributable to you and you alone. For example, your company having failed to win a valuable contract would work well as an answer. If possible, you can go on to outline what was learned from the experience and how this knowledge was put to good use in the future.