From breath to soul
Psyché comes from the verb psychein, "to blow," and named the breath understood to leave a person at the moment of death. The Greeks pictured this departing psyché as a winged, human-shaped figure — a double, or eidolon, of the dead person — passing on to the underworld while still carrying a shadowy kind of existence. The same Greek word, psyché, was also used for the butterfly, drawing a visual link between the departing breath-soul and a winged creature.
This double sense of "breath" and "soul" is not unique to Greek: related words in Hebrew (nefesh) and other ancient languages carry a similar overlap. Psyché is also the root of later words like psychism, psychiatry, and psychology.