An intentional family is formed when a group of people choose to re-create a family, whether official or not, by choosing people to surround themselves with in familial support of each other. When one gets married you are considered to be family with your spouse. This is a relationship that, in theory, one deliberately chose. An adopted sibling can be a close sibling regardless of blood. If there were no concept of intentional family, then no one would be able to say “He’s like a brother to me.”
When one’s family is terribly messed up, and you need healthy familial relationships, often you can choose people who are family with you. It does not matter that they be blood related, but that they share a kinship (kindred spirits), that there is love (of the familial sort), and that there is mutual support being shared. Intentional family can go wrong like any other, but it is also a type of family that it may be easier to cut ties with if necessary.