A personal board of directors is like your own little entourage, and the members of your board should have special expertise (not necessarily a professional) in an area where you're lacking. Anyone who has given you useful advice in the past could be considered for your personal board. A career coach that contributes to the New York Times has this to say:
A personal board of directors is simply a collection of people who know you, are interested in your well-being, and have useful points of view. You consult with them on a regular basis -– say once every six months. It’s unlikely that you will assemble your board members in person, but you do assemble their perspectives.
I read up on the term a bit, and every source I found agreed that your board comes in handy most when you're at a crossroads in your career, or have important decisions to make in which an expert's guidance would help you make the best choice while considering your personal circumstances. They're not there to handhold, they're just there to help you see a bigger picture — their expertise allows you to consider all options in a given situation.