A family is the basic social unit of (many? most? all?) vertebrates. In most animals, the family comprises a female and her dependent offspring. The family unit is temporary and ceases when the young are able to feed and defend themselves. In a few species the young are attended to by both the male and female, but the relationship is still a transient one.
In humans, a family is not restricted to individuals who share DNA. Families are as much social constructs as anything else, and their definition often shares biological, cultural, legal and emotional elements. Because of constantly evolving societies, notions of what, exactly, constitutes a family can have complex legal and emotional ramifications.