This question definitely has a negative connotation, or at least that's how it sounds to most people. It's almost as if the interviewer is fishing to see just how badly you screwed things up in the past, to figure out if you will screw things up once they hire you.
Good news: that's not the reason you're being asked this question.
What the Interview Wants to Know
- Your take on a bad situation. Months or years after making the mistake, how are you reacting to it? Has it affected your performance since then, or do you view it as a part of life?
- Your handling of the situation. This is the true purpose of the question. He wants to know what you did to fix the problem that you created.
- Your ability to learn from your mistakes. If you can show that your mistake helped to make you a better employee, it earns you good marks in the interviewer's books.
How to Answer the Question
The interview wants to know the three things above, so your answer should give him the information they want.
Here's a sample answer you can try:
"In my previous company, I was working with a boss who was always micro-managing my work. I asked him to back off, and he allowed me to make my own decisions. Unfortunately, I was not as prepared as I thought I was, and I ended up losing a big client thanks to a misunderstanding.
This mistake cost our firm a good deal of money, but I learned that most managers/bosses are helping you because they want you to do the job right. They're not trying to micro-manage or get in your business, but they are doing it for your own good. It has helped me to have a great relationship with every boss I have had since then, and I've found they are excellent mentors that make me a much better employee."
See, the answer highlights the situation, the setting that led to your mistake, and what your takeaway was. It's a good way to answer the question truthfully, but without looking like a careless idiot who made silly mistakes.
Remember: Truth May Kill
If you've made a huge mistake in your past, do you really need to tell your interviewer about it? Absolutely not!
Be smart and share a "big" mistake that you can use to spin into a positive outcome, such as the answer above. If you were responsible for some giant fiasco that had no good outcome, then you should consider using another mistake that you can spin positively.
Also, if there is a way to show how the mistake was caused by factors out of your control, it can help to strengthen the answer. It doesn't shift the blame away from you (trying to duck blame makes you look bad) but reduces the proportions of your role in the mistake.
To sum it up: you need to admit your mistakes, but try to spin the outcome for the positive and answer in a way that makes you look stronger for the failure.