Draw the outline of a face, and put an eye inside it — that is 面, exactly as the ancient scribes reasoned it. A face is framed by its edge and defined by its gaze, so one eye stood in for the whole. Over the centuries the frame squared off and the eye inside simplified, but the logic never left: 面 still means both "face" and, by extension, any surface or side something shows the world.
A piece of culture
The face you must not lose 面子 (miànzi), "face", is one of the most important ideas in Chinese social life: a person's dignity, reputation and standing, which can be given, saved or lost in a single conversation. Praising someone publicly "gives face" (给面子); embarrassing them makes them "lose face" (丢面子) — and both are weighed carefully at every dinner table and business meeting. When China simplified its writing in the 1950s, it also folded the separate character for noodles, 麵, into this one purely because they sound the same — so 面条, noodles, now literally reads as "face-strips".
Use it in a real word
面目
miànmù · min6 muk6
face; true colors — literally "face-eye"; you already know 目