If the person's back is showing towards you, their face is looking the other way.
The person was standing in the middle of the clearing, facing away from me.
An object like a cube has six sides or faces and you can use facing to relate its orientation to a particular face. You do this with your example sentence, "...[their] back facing me". But because people actually have one (and only one) face, the verb is unambiguous when it does not qualify another part of the body.
As an aside, "his/her" could be replaced with their. See this question.