Central to Chinese social life.
面子 (face) is one's public dignity, and
给面子 means publicly granting that dignity — by accepting an invitation, going along with someone's wishes, or praising them in front of others. Its opposite
不给面子 ("not give face") is a real social offense and a common complaint about a rude relative or colleague. Common patterns:
给我点面子 ("cut me some slack"),
给…
面子 ("do … the courtesy"),
太不给面子了 ("that's so disrespectful").