Fictive kinship is the practice of creating a family bond 2 between people who are not related by blood. This was practiced by slaves, who were broken from their normal family ties when taken over the Middle Passage, as well as used on a normal basis to define the bonds between close friends and clan members in many cultures. It is recognized in religious communities such as monasteries and convents (Mother Superior, Pope). Fictive kinship in the western world (where a blood tie is often considered to be the only true family tie) is sometimes a coping mechanism for when your own family members are non-existant or non-functional.
Good examples of fictive kinship include:
A runaway that lives with a college-age couple and their dog and considers them to be older siblings
A family reunion that consists of one nuclear family and their close friends ("Aunts" and "Uncles"), especially when it is societally normal to call them as such (thank you StrawberryFrog)
A rock band on tour that is so closely knit they can anticipate eachother's needs and wants
A family bond would be a familial connection acknowledged by both parties, and with both parties actively taking part in the accepted roles of the assumed family member.