Israel Zangwill wrote a century ago that “Life is Janus-faced, and the humorist invests his characters with a double mask; they stand for comedy as well as for tragedy.” Janus, a Roman God, has the image of a man with two faces, looking forwards and backwards. Read more about him here .  It seems obvious what the phrase means when used today. A person is portraying two distinct personalities, at least one of them deceitful. In case you weren't sure, it's not a compliment. 

Ever eat egg and get some yolk on your face? It can be kind of embarrassing. An embarrassing situation can be called getting caught with egg on your face. ( source )

Especially important in Asian cultures is the idea of saving face. You can read about the origin of this phrase here . The phrase means to protect, shelter, or save someone's reputation.