A loss of one's honor. A person can lose face by being proven wrong, by not living up to expected potential, or by acting dishonorably.
Different cultures have differing reactions to loss of face. In North American culture, a loss of face is usually only an embarrassment. Some cultures have traditionally associated loss of face as a dishonor on the entire family, and the only way to make restitution could be through a formal public apology, or in extreme cases, suicide.