What does it mean to "lose face"?

Its an Oriental saying meaning that one is embarrassed or humiliated

"face" means your position and how you are evaluated by your peers, by those around you. to lose face is to suffer a devaluation of that esteem. that is, others think less highly of you because of whatever it was. It is often embarassing to lose face, but that is not the act of losing face, it is the result. Embarassment is shame at yourself, you did something that you are ashamed of. Losing face generally involves having done something that should be shameful, for which you should be embarassed.

Only a person that doesn't care what others think of them would be free of shame. Such a person would have no real "face" to lose.

to be embarrassed/ humiliated in front of your peers and lose credibility.

E.g. If my new theory gets disproved by Thomash tomorrow in front of my physics students I stand to lose face.

It means to lose creditability.

It means to suffer a humiliaton.

Your pride has been punctured.

Your honor has been tainted.

You are embarrassed to raise your head.