Answer by Jason Yeaman:
It's a user group affiliation where the 'head of family' is the administrator with a credit card.
He can invite other appleIDs to join his family, and any apps he buys, get shared with those in his family.
He can also create Apple ID accounts, make them part of his family, then give those IDs to people like kids.
Basically family sharing is a purchase centric authorization model that uses one person as the POC for app purchase authorization, user administration, and application dissemination.