What is Non-Binary?

Non-Binary is a term that literally means "not two choices." There can be one choice or three or more choices but there can't be exactly two.

But I'm confused as to what it means when applied to gender.

I say gender and not sex because sex and gender are different things. From the American Psychological Association: 

"Sex is assigned at birth, refers to one’s biological status as either male or female, and is associated primarily with physical attributes such as chromosomes, hormone prevalence, and external and internal anatomy. Gender refers to the socially constructed roles, behaviors, activities, and attributes that a given society considers appropriate for boys and men or girls and women." 

If you don't understand this you're going to always be confused. Also, a lot of people appear to be equating non binary and gender fluid. The latter is as least feasible because gender nonconformity has been a thing for a long time. But I have no idea what Non-Binary means.

Ignoring Intersex, there are only two sexes and therefore by definition only two genders. So what the hell is Non-Binary?