This has been a pain for myself and my oldest child (who is also non-binary). We do have to repeatedly explain it to my parents who still struggle to fully grasp it. A couple things that have been helpful for me:
1. I try affirm for them that it's ok not to understand. I try to avoid making them feel they have to walk on egg shells by correcting everything they say that is "wrong" or "potentially offensive".
2. Related to #1, I also try to keep in mind their perspective. They're in their 60's and 70's and have an entire life in which they never really were exposed to gender identity the way we are today. Gender has always been a binary thing for them and after 60+ years, that's a lot of unlearning to do. So again, I try to be affirming and understanding of their struggles and I accept they may never totally "get it".
3. I try to focus on how it feels for me. Rather than try to explain the concept of non-binary, I focus on what they really want to know, what is it that I'm feeling. I explained to my mother how there are days where I feel like I should have been born with a female body and that there are other days that I just feel like I'm somewhere in between. I hate to say it but I do use examples from contemporary culture to compare and contrast my experience, people like Caitlyn Jenner, Laverne Cox, and Carmen Carrera. These are people they see and understand so it allows me to set some context that they can associate with to some degree.
For Christmas, my oldest bought my mother a book called Gender Identity for Beginners. It was a book they used in her gender studies class at school and she hoped it would help my mother better understand. I'm waiting to hear how that was received. If my mom understood her desire to help or if she's offended and feels that my child was being a smartass.
