The expertise of individuals is considered more valuable than the organization.
Person Cultures are typically found in professional partnerships, at least in the past. Here, the lawyer or the doctor or the accountant who leads a practice is the king (or queen). They are the 'rainmakers' (bring in the clients), although they may or may not have the expertise to deliver the services. Person Culture organizations are interesting places to work because they can be loose collections of practices, each with their own resources (employees) and not sharing much more than office space. (I once consulted for the ultimate Person Culture organization: 10 partners who shared nothing but the name on the door. They had a dozen different ways to charge each other for common items like rent, copiers, electricity, insurance, etc. It was chaos and not at all fun for the employees).
Person Cultures differ from Power Cultures in that they are a collection of fiefdoms which aren't arranged into a single hierarchy.
If you want to work in a small law or accounting office, you'll be working in a Person Culture.
Would this culture be a good fit for you? Take this quick assessment to find out.