1.
to show up, to make an appearance, to drop by
To attend briefly or make a short visit, often to acknowledge an obligation or maintain relationships.
2.
to peek out, to appear (literal)
For something to physically emerge or become visible.
Structure: 顔 (face) + を + 出す (to put out) — literally 'to put one's face out'.
SENSE 1 — SHOWING UP: A brief appearance, with no expectation of staying. It is the standard way to talk about turning up at something out of obligation or goodwill: a meeting, a party, a relative's house. Saying 顔を出す rather than 行く signals that the visit is short.
SENSE 2 — PEEKING OUT: Used of anything that physically emerges into view — the sun through 雲, a 芽 pushing through the soil, an animal at the mouth of a hole. The subject is normally inanimate or an animal, and no face is involved; the phrase simply keeps its literal image.
Related words
OTHER 顔 EXPRESSIONS: