It literally means what it is. Homo means the same, faux is french for false and asexual means to not want sex. Altogether it means, to be gay or lesbian but in a false way for your and your friend's amusements; pretend to be gay or lesbian and refer to your friends as your boyfriends/girlfriends when you clearly are not, and have no desire to have sex with them, although you pretend to be, just for the sake of fun.
This is clearly shown in GIRL'S SECONDARY SCHOOLS.
Tina: I like staring out windows.
Hayley: You are so weird. I just wanna run away from you right now.
Tina: Nah, you know you have the hot's for me really
Hayley: You are so homofauxasexual.