Your McKinsey interviewer really wants to hear an answer to this question. It will not be asked directly, but she will guide you there with the questions like “and what do you think he felt?”, and “how did you react?”, etc.
Essentially, for a consultant it’s important to be able to convince people not only with a sheer force of the numbers and logic, but also with a bit of a “human touch”, meaning understanding people and not being a boring machine :)
So, once you think about the stories you are telling during the interviews, try to highlight some interpersonal details (like “he had a rough time with his family at home, so I offered to take over his work for the next two days”, or “she really liked French instrumental music, so I organised this team event at the concert hall”, etc.). Try to highlight how you pay attention to what people like, what upsets them, how they tick in general – and how you use this knowledge to steer people into the right direction and to achieve the results you want (it sounds a bit psychopathic, but it’s a reality of consulting business hahaha). The interviewer will give you a good amount of bonus points if you will be able to showcase your human side during the interview :)