Family of origin are the people who we are born into, or marry into. While Family of Choice are the people that we choose to have involved in out lives. These people will become like siblings, uncles, aunts or even surrogate parents for us.
In fiction family of choice is often used to help create a family with people that they have more in common with, especially when the main character has developed some type of supernatural powers. The new family share similar powers or secrets.