What does it mean to have an old soul?

Wisdom. Some people might use the term "old soul" to describe a person who seems very wise about life, self, and others. They have a spiritual view of things, understanding that there's much more to others than appears on the surface. They have the patience to listen, and allow others to be who they are without judging. It usually feels good to be in the presence of such people, and we seek them out.