How do I explain being trans to people that know nothing about it?

I recently had to explain being trans to different people (police, teachers, parents, etc.), that knew little to nothing about being trans. I had a hard time trying to explain it, without landing in the "born in the wrong body" and "identifying as something" territory. And the medical way was too complicated to explain in a short amount of time, and even there, I'm not sure how I should phrase it best.

Is there any easy and short way to explain being trans to someone, without it sounding weird?