Decided to do as little research into this nonbinary crap Nora refuses to quit shitting the bed over.
First, a surprisingly levelheaded comment on the subject from someone who identifies as this on Tumblr, of all places:
Short version is that there is hardly any literature on the subject, most of the world considers the subject bullshit at best, and most current evidence doesn't really support it on a biological basis.
Next, a reddit thread where someone asks about the subject and get a bunch of answers, ranging from Nora style fruitcakes who ask you listen and believe them, fuck science, to people who try to be helpful.
https://www.reddit.com/r/ainbow/comments/3dzdhw/is_there_any_evidence_that_nonbinary_genders_exist/
The most science has done is discover some brain tissue anomalies in the brains of some transgender people, but the evidence is not conclusive because wide ranging studies haven't been conducted on the brains of both binary and nonbinary identifying people in enough numbers and studies to better determine if this shit actually has validity.
http://www.pinknews.co.uk/2011/01/26/scans-show-difference-in-transgender-brains/
According to this study, it's very small, one study, and at best, speculates there may be some biological differences in the brain for people like this, but nothing conclusive can be inferred so far aside from coincidental data without further study.
As an interesting sidebar, someone with the name "Me" had an amusing chimpout in the comments.
And here's a PDF by someone who actually did some study on the subject:
http://www.ala.org/glbtrt/sites/ala.org.glbtrt/files/content/professionaltools/Nonbinary Gender Identities in Media Annotated Bibliography.pdf
Nonbinary gender definitely is considered a sociologically acknowledged condition, but is not based in biological terms like biological sex, and is understood as a conscious decision based on the choice of the person who identifies as nonbinary.
In simple terms, Nora is biologically female, but she can call herself nonbinary if she feels that way, but her feels don't trump the fact, genetically speaking, she was born female (as far as her genitalia are concerned), and since to all known knowledge Nora is not intersex or actually male, then, unless Nora feels like showing medical documents showing some genetic abnormalites she hasn't told anyone about, only one conclusion can be drawn based on all this information.
Nonbinary, as a term of gender identity, means you feel neither male or female, but is not backed by biological fact to this date due to lack of scientific evidence.
tl;dr: It's a legit term that Tumblrtards have bastardized for their own purposes and means jack fucking shit from a biological standpoint, meaning Nora was born and will die female, no matter what the fuck is going on inside her head, unless she decides to get an actual sex change.