“Psyche” refers to soul, self, and mind in Greek, hence its similar meaning in English; thus we also have psychology, psychic, etc.
In Greek mythology, Psyche was Eros' (Cupid's) mortal beloved. Psyche endured many trials foisted on her by Eros' mother Aphrodite (Venus), jealous of Psyche's beauty. This included a trip to the underworld. Eventually Zeus sanctioned the marriage of Eros and Psyche, and granted Psyche immortality.
In her sojourn to Hades, Psyche succeeded in retrieving a bit of Persephone's (the queen of the underworld's) beauty, in a box Aphrodite had given her. This box is sometimes confused with Pandora's jar (Pandora's "box"), as in the left image:
Bernardo Daddi (1512-) engraving after Raphael                                             Paul Alfred de Curzon, (c.1840-1859)
Upon returning, Psyche tried to sample a little of the contents of the box. This put her in a deep sleep, from which Eros eventually awakened her with a kiss.
John William Waterhouse, c.1903                                     Sir Edward Coley Burne-Jones (c. 1871)
They lived happily ever after their wedding, with the physical (Eros) and spiritual (Psyche) joined at last.