Ok, this is a HIGHLY abbreviated overview that I'm sure other LGBTQ+ folks would say doesn't get it exactly right:
If we decouple the idea of gender (societal expectations for men/women -- e.g. boys like blue, girls like pink. Boys wear shorts, girls wear skirts.) from the idea of sexual/genetic characteristics, then we can start to discuss what it means to be a man vs what it means to be male.
Manliness and femininity are both spectrums -- you can imagine folks who are real tough manly men and folks who are not. We call these two spectrums the gender binary -- people typically fall into the manly spectrum somewhere, or in the feminine spectrum somewhere.
Nonbinary folks feel excluded by those spectrums for one reason or another. Nonbinary is an umbrella term that can include people who are agender (e.g. I don't identify with any gender), genderfluid (e.g. sometimes I feel masculine, sometimes feminine), genderqueer (e.g. I'm going to take the elements from each spectrum I like and make my own thing), etc.
For a more concrete example, people like David Bowie are often held as icons for the nonbinary community (again, not everyone agrees with me here). Eddie Izzard also famously played with gender. Ruby Rose and Tilda Swinton identify as genderfluid. There's a lot of different people under the broad umbrella of nonbinary.
> Can you share some experiences?
I've been told, "Your pronouns don't matter". I've had my bathroom use policed (I often feel uncomfortable in mens/womens restrooms and strongly prefer gender neutral spaces). I've had coworkers ask, "So does that mean you fuck men?" in a way that is clearly a set up to a joke.
Every day I make a conscious choice on my presentation (clothes, hair style, etc.). I typically choose to present in a masculine way because it makes my life easier, even though it's a presentation I am less happy with. There's a surprising amount of cognitive load for me for something that's relatively mindless for most people. Do I dress in a way that makes me happier, but results in a lot more sideways glances (and possibly violence?) or do I dress in a way that keeps me safer but less happy?
I understand that they/them pronoun use is not common, and I'm never upset when I correct people, but some people have told me, point blank, "Your pronouns are wrong and gross" or "I will use they/them, but you should know I'm lying to your face when I do so."
These sorts of experiences are distractions from what I really want to do, which is build awesome engineering teams and solve hard technical problems. But they're unfortunately a reality of (at least) the software world in the US and most likely in the broader workplace.