late 13c., meven, in various senses (see below), 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."
Of the physical meanings, the earliest in English (late 13c.) is the intransitive one of "change one's place or posture, stir, shift; move the body; move from one's place, change position. That of "to go (from one place to another), journey, travel; set out, proceed" is from c. 1300. The transitive sense of "cause to change place or position; shift; dislodge; set in motion" is from late 14c., as is that of "impart motion to, impel; set or sustain in motion." The intransitive sense of "pass from place to place; journey; travel; change position continuously or occasionally" is from c. 1300.
The emotional, figurative, and non-material senses also are mostly from Middle English: The earliest is "excite to action; influence; induce; incite; arouse; awaken" the senses or mental faculties or emotions (late 13c.); specifically "affect (someone) emotionally, rouse to pity or tenderness" by early 14c. Hence also "influence (someone, to do something), guide, prompt or impel toward some action" (late 14c.).
The sense of "propose; bring forward; offer formally; submit," as a motion for consideration by a deliberative assembly" is by early 15c. Sense of "to change one's place of residence" is from 1707. In chess, checkers, and similar games, "to change the position of a piece in the course of play," late 15c. Commercial sense of "sell, cause to be sold" is by 1900.
The policeman's order to move on is attested by 1831. To move heaven and earth "make extraordinary efforts" is by 1798. Related: Moved;moving.
mid-15c., "a proposal" (a sense now obsolete), from move (v.). From 1650s in chess, checkers, etc. Meaning "act of moving from a stationary position, a change of position or relation" is by 1827. Meaning "a change of habitation" is by 1853. Meaning "a particular action or motion" is by 1939. Phrase on the move "in the process of going from one place to another" is by 1779; get a move on "hurry up" is American English colloquial from 1888 (also, and perhaps originally, get a move on you).