Gender terms

I’m not asking this to be rude. I’m just searching for clarification on what it is. Them/they. When someone wants to be addressed as them/they what does this mean? Are they male? Female? Both? Neither? Also what is binary? What are enbies? If you identify as something other than straight, gay, lesbian, bisexual I would love to hear what you identify as, why and what makes you feel that way (or how you discovered it). My partner and I were talking today and points were made about people’s psyche and why one might feel one way. Since I don’t have anyone really close to me who identifies as something other than the “basics” (sorry don’t know how else to word that) I’d like to hear how others explain it. Thanks!