The HR professional isn't interested in hearing about that time your co-worker said something snide about you in the kitchen, or when your manager overheard you gossiping about a client to a friend.
Instead, this question is asked to gain insight into how you handle professional conflict. At the office, conflict is bound to arise, particularly when you're working closely with many different people. It's critical you know how to handle conflict without pointing fingers. Your answer should primarily focus on the solution, and should show a level of empathy towards your colleagues, rather than focusing on the problem.
You might say something like, "I had a deadline I needed to meet, and I was working with a designer who promised me her designs in time. When the deadline approached, my designer wasn't ready. It made us both look poorly in front of our clients. To resolve the issue, I discussed the problem privately with my designer. She told me she was stressed out and overwhelmed, and simply needed another week on the project. I told her that was fine with me, but in the future, we needed to be transparent and honest with each other. Moving forward, we established guidelines and became more efficient teammates."