相 = 木 (mù, tree) + 目 (mù, eye). An eye set beside a tree: the picture is of looking, of inspecting a thing closely. The Shuōwén reads it as 省视, to examine and view. The radical is the eye 目 on the right, and the tree 木 on the left supplies the scene being looked at. The glyph is identical in simplified and traditional script, so the two hero panels show the same form.

From that single act of looking, two readings split apart, and the split carries the meaning:

Level tone, xiāng: mutual, each other. When two parties look at one another, the looking becomes reciprocal. This reading marks an action done back and forth between sides: 互相 hùxiāng (mutually), 相同 xiāngtóng (the same), 相信 xiāngxìn (to trust), 相反 xiāngfǎn (opposite).
Falling tone, xiàng: appearance, to examine, minister. When the looking settles on a fixed object, 相 becomes what is looked at and the one who looks. It names the appearance or photograph (照相 zhàoxiàng, 相貌 xiàngmào), the act of inspecting a person (相亲 xiāngqīn, the matchmaking look), and the high official who oversees the realm (宰相 zǎixiàng, 首相 shǒuxiàng).

The thread is the gaze. Turned outward toward another, it is reciprocity; turned onto a single object, it is the face that is seen, the act of sizing up, and the minister whose whole office is to look over the affairs of state. One eye on one tree, branching into mutual and into mien.

Read in the falling tone, xiàng turns from an action between people into the thing that is seen. It is the appearance, the look, the face: 相貌 xiàngmào (a person's looks), 长相 zhǎngxiàng (facial features), 真相 zhēnxiàng (the true face of a matter, i.e. the truth behind it).

The same reading names the captured image. 照相 zhàoxiàng is "to take a photograph," literally to shine a light and fix the appearance; the picture itself is 相片 xiàngpiàn or 照片 zhàopiàn, and the device is the 相机 xiàngjī (camera) or 照相机 zhàoxiàngjī. Listen for the tone: the mutual xiāng of 互相 rises level, while the appearance xiàng of 照相 falls. The shift in tone is the clearest signal of which 相 you have met.

The Shuōwén gloss, 省视 (to inspect, to look over), survives most plainly in two falling-tone uses. The first is the verb of sizing-up: 相亲 xiāngqīn is the formal meeting where a prospective couple look each other over with marriage in view, and 看相 kàn xiàng is to read a face for character or fortune. To 相 someone is to examine them.

The second is the office. The 宰相 zǎixiàng was the highest minister of the imperial court, the one whose duty was to look over the affairs of the realm on the ruler's behalf. The word carries into modern usage as the title for a foreign head of government: 首相 shǒuxiàng (prime minister) and 丞相 chéngxiàng (chancellor) belong to the same family. Across all of these, the falling-tone 相 is the gaze that inspects, weighs, and oversees.

Picture an eye, 目, standing beside a tree, 木, and looking hard at it. That gaze is the whole character. Now let the gaze move two ways.

Turn it toward another person who looks back, and the looking becomes mutual: you trust each other (相信), help each other (互相), share the same view (相同). Read it level, xiāng. Fix it instead on one object, and 相 becomes what the eye rests on: the appearance and the photograph (照相, 相片), the face that is the truth of a thing (真相), the act of sizing someone up (相亲), and the minister whose office is to look over the realm (宰相). Read it falling, xiàng. One eye on one tree, opening into mutual on the one hand and into mien on the other; the tone tells you which way the gaze has turned.