A multiple-adult family (MAF) is a family which is headed by more than two co-equal adults. The family may or may not have children (and may or may not want any), and any sexual relationships within the family may or may not include all the adult family members. (In other words, membership in the family does not imply a sexual relationship with others in the family.)
This type of family is distinct from polygamy, where all members are involved in at least one sexual relationship, and especially distinct from polyandry and polygyny (two sub-types of polygamy) which involves sexual relationships between one person of a particular gender and two or more others of the opposite gender.
Multiple-adult families have become something of a taboo subject, despite the fact that larger families consisting of multiple generations, distant relatives, "cousins" who weren't actually related, etc. used to be much more common in Western culture and the United States in particular.