Non-Trinary or Non-Ternary refers to someone whose gender does not fall strictly within the gender trinary/ternary (man, woman, and neutrois). Anyone who is not always, solely, 100% male, always, solely, 100% female, or always, solely, 100% neutrois can be considered non-trinary. Some non-trinary people may identify with one or more of the trinary genders, at least in part.
Non-trinary can be a gender identity on its own, or it can be used as an umbrella term for anyone whose gender is something other than male, female, or neutrois.