As the name implies, it’s when the entire family goes to a counselor or a team of counselors. Mom and Dad are seen as a couple, or a subsystem. The children are also a subsystem. In a family of four, if the two children are opposite sex, Mom will relate differently to her daughter than she would to her son. Dad would relate differently to his son than his daughter.
As everyone knows, there are a lot of reasons why the whole family might see a counselor. One reason is that one member might have an issue, but the whole family needs to know specifics about the disorder, so they can help the afflicted member remain healthy, and not relapse.
In some cases, when the entire family comes (for example) it might be because a younger teenage daughter is anorexic. But in talking to all the family members, the therapist finds that the parents are fighting a lot. The daughter feels threatened, and believes that if she stops eating, it may bring the parents together, and they will stop fighting. She creates a problem in herself, to change the focus of the family dysfunction. The therapist helps the parents solve their problems, and the daughter begins eating again, because there isn’t a reason to starve herself, any longer.
(the above is just an example of why a family might all go to one therapist, for counseling. It is not intended to be a diagnosis of any kind.)