As a noun 相 covers everything to do with outward form: a face (长相), a photo (相片), a stance (亮相), even a state of a wave (相位). The 'minister' sense comes from the official whose job was to look over state affairs — 首相, 宰相, 丞相.
culture
看相 is traditional Chinese physiognomy — reading character and fortune off a face or palm (手相). Still common at temple fairs and on dating-app profiles. Pair it with 属相 (your zodiac animal) and you have a full folk-astrology kit.
Right side 目 (eye) — Kangxi radical #109. The eye on the tree picks out an outward form — a face, a photo, a wave's phase, even the bearing of a minister inspecting state affairs.
Left side 木 (tree) — the original object being inspected. The act of judging a tree's quality became the abstract 'judge by appearance' that powers 相 (look, photo, minister, physiognomy).
