This refers to people whose gender identity does not correspond to the spectrum of female and male gender binaries. Non-binary people can feel that their gender identity is: androgynous, in between feminine and masculine, neutral or unrecognized, multiple, partial, or culture specific.
Many non-binary people do not use the he or she pronouns because they feel uncomfortable; others might use those pronouns despite not completely identifying with them. In English, they is often used as a gender-neutral pronoun. In Spanish, however, there is no official translation, although in some cases, elle is used (as an alternative that combines él and ella).
The term non-binary person can be confused with queer person or genderqueer person. However, though they may be similar, they are not the same. The term queer person has a political and social connotation associated with sexual dissidence, while a genderqueer person entails a series of experiences that encompass each one of the gender identities and expressions that are part of it, without specifying which one. Some genderqueer people call themselves a man woman or a woman man to identify themselves and give it a political connotation; that is why it is associated to the trans community.
References:
Chicago Healthy Adolescents & Teens
National Geographic en Español
Photo credit: Tatyana Okhitina