Facepalm, also known as "facepalming," refers to the act of placing one's face in one's hands, a form of nonverbal-communication common among many cultures. The action conveys a message of dismay and is often a reaction toward someone's momentary lapse of logic, judgement, or memory. This reaction may be directed toward another person or be self-deprecating.
Picard covered his face with his hand when he was vexed to once again encounter the troublesome Q in season 3 episode Deja Q. The clip was uploaded to YouTube in 2007, and now the screengrab used to represent a facepalm moment is everywhere.