late 15c., mappe "bundle of coarse yarn, cloth, etc., fastened to the end of a stick for cleaning or spreading pitch on a ship's decks," perhaps from Walloon (French) mappe "napkin," from Latin mappa "napkin" (see map (n.)). Modern spelling by 1660s. General sense, of such an implement for cleaning floors, windows, etc., is from 1610s. Of smaller utensils of the same sort used for cleaning dishes, etc., by 1869. Of anything having the shape or appearance of a mop (especially hair), by 1847. Grose ["Dictionary of the Vulgar Tongue," 1788] has mopsqueezer "A maid servant, particularly a housemaid."
"rub or wipe with or as with a mop," 1709 (in mop up), from mop (n.). Related: Mopped; mopping.
Old English up, uppe, from Proto-Germanic *upp- "up" (source also of Old Frisian, Old Saxon up "up, upward," Old Norse upp; Danish, Dutch op; Old High German uf, German auf "up"; Gothic iup "up, upward," uf "on, upon, under;" Old High German oba, German ob "over, above, on, upon"), from PIE root *upo "under," also "up from under," hence also "over."
As a preposition, "to a higher place" from c. 1500; also "along, through" (1510s), "toward" (1590s). Often used elliptically for go up, come up, rise up, etc. Up the river "in jail" first recorded 1891, originally in reference to Sing Sing, which is up the Hudson from New York City. To drive someone up the wall (1951) is from the notion of the behavior of lunatics or caged animals. Insulting retort up yours (scil. ass) is attested by late 19c.
1550s, "to drive and catch (swans)," from up (adv.). Intransitive meaning "get up, rise to one's feet" (as in up and leave) is recorded from 1640s. Sense of "to move upward" is recorded from 1737. Meaning "increase" (as in up the price of oil) is attested from 1915. Compare Old English verb uppian "to rise up, swell." Related: Upped; upping. Upping block, used for mounting or dismounting horses, carriages, etc., is attested from 1796 (earlier was horsing-block, 1660s).