This question is important to ace because it helps an interviewer understand how you deal with conflict. It also helps test how well you think on your feet–so if you prepare ahead of time with a specific example, you’ll avoid the awkward moment of silence while you try to think of an example.
Once you have an example in mind, simply explain what happened, how you resolved the issue in a professional manner, and try to end the story with a happy note about how you reached a resolution or compromise with your co-worker.
Conflict is part of life, and unless you’re exceedingly lucky and don’t have to work (why are you reading this?) then it’s also part of your work life. I mean, life is a whole series of conflicts, and how you resolve them says a lot about who you are as a person — which is why interviewers love to ask you about it, usually in one of these forms:
Tell me about an assignment when you had to work with someone difficult.
Tell me about a time you had a conflict at work.
Give an example of a time you had to respond to an unhappy customer or coworker.
Tell me about a time that you disagreed with a manager.
And I’m sure that if you put your mind to it, you can think about a time you’ve had to deal with a… shall we say, fly in the ointment. Thorn in your side. Pain in your ass. A real turd sandwich.
They ask this question to gain insight into your behavior, interpersonal skills, and your overall ability to manage conflict — not to learn about how much of a jerk your former coworker or customer was.