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.