I went looking for the term to make sure that I knew what I was talking about. In Pragmatics (a branch of linguistics), face is "the public self-image of a person. It refers to that emotional and social sense of self that everyone has and expects everyone else to recognize". I'm pulling this from Pragmatics by George Yule. He also talks about face wants being that someone's public face wants won't be unduly threatened. One can also talk about a face-threatening act or a face-saving act.
There's much more in this book that I want to talk about but my deploys are done, so I'm leaving work.