McKinsey looks for three things: i) Hard skills: ability to learn, ability to structure problems, control over basic algebra ii) Soft skills: ability to interact well with the clients, peers, team members and bosses iii) Cultural fit: this one is the most tricky one. Some people can do an amazing job but for some reason don’t fit well with the culture of the company. They may be too loud or too shy for example. I hear that McKinsey today is much more tolerant on the different personality traits it expects from its employees, but there is still a standard McKinsey way of behaving.
At McKinsey, you need to be hypothesis-driven, quick thinking, and have a "do-er" attitude. Quantitative and analytical thinking are also musts. Some of the more underrated skills that I didn't appreciate, but that are actually incredibly important for the job, are great email communication, emotional maturity, and empathy with people / clients. At McKinsey, you will often have to deal with clients that are not happy that you are there. It takes a great amount of emotional sensitivity to know how to navigate these situations.