What does this idiom mean: "to lose face"?

[Rusalka]

Test No. incompl/inter-61 "Losing It (1)", question 1

He's one of those people who can't bear being seen to be wrong in fact of losing ..........

(a) looks
(b) appearance
(c) face
(d) looking

Test No. incompl/inter-61 "Losing It (1)", answer 1

He's one of those people who can't bear being seen to be wrong in fact of losing face.

Correct answer: (c) face

Your answer was: incorrect
He's one of those people who can't bear being seen to be wrong in fact of losing appearance.
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Hi! What does it mean _loosing face_
Hello to everybody

[Alan]

Note the spelling LOSING. This means LOSING self respect.
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English as a Second Language
You can read my ESL story A day in the life of a flat hunter