Proper Noun: Typically, this title is bestowed to an ugly and/or fat girl who has been systematically rejected by nearly all non-gay males for a significant portion of her life.
To those who do not fit the aforementioned demographic, some other psychological or emotional problem has likely manifested itself, causing normal romantic developments with non gay males to become problematic at best.
To counteract this state of affairs, the fag hag attaches herself to homosexual males (normally of the extreme flamer variety). Psychosocial data suggests that this is a passive relationship that begins out of fear of rejection, but can often progress to full blown dementia, dullusional or irrational behavior patterns, or obsessive compulsion.
Though not an officially recognized neurological or psychological disorder by the DSM (Diagnostic and Statistical Manual of Mental Disorders), hundreds of case studies documenting the behavior have been submitted to the American Medical Association and the American Psychological Association for further review.
As of this writing (NOV 2010), no official response has been issued by these governing bodies, but many speculate that fear of social stigma or notions of political correctness have acted as a significant barrier to further study.
Psychiatrist: "So how long have you been acting as a fag hag"?
Patient: "I am not a fag hag, and that term offends me. I just choose to surround myself with only gay men. Your obviously nothing but a homophobe. It is you who have the problem......"