Most jobs require you to get along with different types of people. Some of your coworkers, managers, and/or clients will turn out to be idiots, slackers, and/or weirdos. Disagreements are bound to arise.
To succeed at work, you must be able to deal with conflict professionally. This is particularly true in certain jobs (project management, customer service, law) and in certain company cultures.
Your interviewer wants to get a sense of how you will respond to conflict.
Candidate should appear to know how to convince others that their point is right. Sees conflict as natural. Never personalizes it, but explains the issues involved forcefully; stands up for what he believes is best for the business in a logical and reasonable manner.
You basically want to hear that they do not like to point fingers at others; that they try to stop the mistake from happening again by making his/her colleague aware of their error in a non blame educational manner.
Job seeker should explain that they put the team first; should not appear easily intimidated; seeks to resolve differences; does not personalize conflicts.
Answer given should show you that the candidate can stick with it and work through negativity quickly.
Job seeker should appear to know how to resolve issues and uses it as an opportunity to reinforce interpersonal relationships; concentrates on the issues and never personalizes things.
Disagreeing with a supervisor or professor does not make you unemployable. The interviewer wants to know how you expressed your disagreement and whether the conflict caused an impasse or a disruption in the work environment.
Candidate should show that they are helpful in resolving conflicts by understanding each co-workers view of the situation.
Job seeker should explain that seeking clarification is alright; that they try to clarify things to make sure the job is done right; should see conflict as natural and not a personal attack.
Consider situations in past jobs that involved arguments or disagreements. A miscommunication with a coworker may have angered you because it led to a negative review from your supervisor. A supervisor's unwillingness to give you time off may have caused you to miss your friend's wedding. Scan your work history for such examples.