A term used in the transgender/genderqueer communities meaning 'Female, Assigned At Birth'. It means what it says -- a person who was labeled as a female because they were born with a girl's body. The standard counterpart is MAAB ('Male, Assigned At Birth'); there is also the rare designation UAAB (Un-Assigned At Birth).
While any person might use FAAB or MAAB to refer to their 'original' gender, it is used almost exclusively by genderqueer or transexual persons. People that identify with their cisgender do not concern themselves with such distinctions. Because the term is nearly always used by people who feel that this assignment was a mistake, the acronym CAFAB is sometimes used instead -- 'Coercively Assigned Female At Birth'.
On its own, the label FAAB does not tell you anything specific about a person's gender or sexuality, although it does suggest that the person no longer identifies as primarily female.