Interpersonal skills are about being open to and trusting other people, and being able to co-operate and work with others. They deal with emotions and assumptions, and the ability to understand the needs and wishes of the people you work with. While the work can be tough and tedious, such people usually do the best work. With a capable leader, you also get a charismatic and capable force.
Every day, you are likely to come in contact with several different types of people, each of whom is interested in something different. Even within a company, you'll find that you'll be dealing with a variety of different people.