Cover up embarrassment: when a person feels embarrassed, he can make a face-covering expression, because although the face-covering expression is full of tears, the corners of his mouth are smiling, which can reflect an embarrassing feeling.
Expressing self-mockery: Covering your face may be a way of self-mockery. For example, when talking about your shortcomings and doing something wrong, you can show a feeling of embarrassment and helplessness.
Laughing and crying: The expression of covering your face can also indicate a state of crying and laughing, because the expression of crying and laughing can reflect complex emotions and feelings of crying and laughing.