late 13c., from Anglo-French mover, Old French movoir "to move, get moving, set out; set in motion; introduce" (Modern French mouvoir), from Latin movere "move, set in motion; remove; disturb" (past participle motus, frequentative motare), from PIE root *meue- "to push away."
Intransitive sense developed in Old French and came thence to English, though it now is rare in French. Meaning "to affect with emotion" is from c. 1300; that of "to prompt or impel toward some action" is from late 14c. Sense of "to change one's place of residence" is from 1707. Meaning "to propose (something) in an assembly, etc.," is first attested mid-15c. Related: Moved; moving.