1570s, "a (social) moving, stirring, agitation," from Middle French émotion (16c.), from Old French emouvoir "stir up" (12c.), from Latin emovere "move out, remove, agitate," from assimilated form of ex "out" (see ex-) + movere "to move" (from PIE root *meue- "to push away"). Sense of "strong feeling" is first recorded 1650s; extended to any feeling by 1808.

EX- (a Latin prefix meaning “out” or “away”) indicates the force-full separation and distancing of one Thing from another Thing. This indicates a physical process. The Latin root MOV/ MOVE/ MOVERE also indicates a physical shift; a Thing, that had been placed here, is now placed there. So, the combination of these morphological elements creates a word that can be used to describe the act of pushing or moving of Something into an Away Place.