The phrase "brain child" refers to an original idea or creation that comes from one's own mind. There are several synonyms to describe this term that convey similar meanings. For example, the words "brainwave" and "eureka moment" both describe a sudden realization or breakthrough that leads to an innovative idea. Another synonym for brain child is "inspiration," which refers to the source of creative energy that inspires someone to develop a new concept. The terms "vision," "concept," and "invention" are also often used to describe a person's brain child, highlighting the ingenuity and originality of their idea.