The basic definition of portrait photography is the photography of a person or a group to capture the personality of the subjects using lighting, backgrounds and posing.
Well, that sounds rather simple.
In one way, it's simple. You know your purpose when you look at that definition. You want to capture the personality of your subject in a photograph. The problem is that everyone has a bit of a different personality. If you truly want to capture the personality of your subjects, then you need to vary your approach during each portrait session.