mid-13c., "tract of land enclosed as a preserve for beasts of the chase," from Old French parc "enclosed wood or heath land used as a game preserve" (12c.), probably ultimately from West Germanic *parruk "enclosed tract of land" (source also of Old English pearruc, root of paddock (n.2), Old High German pfarrih "fencing about, enclosure," German pferch "fold for sheep," Dutch park).
Internal evidence suggests the West Germanic word is pre-4c. and originally meant the fencing, not the place enclosed. It is found also in Medieval Latin as parricus "enclosure, park" (8c.), which likely is the direct source of the Old French word, as well as Italian parco, Spanish parque, etc. Some claim the Medieval Latin word as the source of the West Germanic, but the reverse seems more likely. Some later senses in English represent later borrowings from French. OED discounts the notion of a Celtic origin: Welsh parc, Gaelic pairc are from English.
Meaning "enclosed lot in or near a town, set aside and maintained for public recreation" is attested from 1660s, originally in reference to London; the sense evolution is via royal parks in the original, hunting sense being overrun by the growth of London and being opened to the public. It was applied to sporting fields in American English from 1867.
New York's Park Avenue as an adjective meaning "luxurious and fashionable" (1956) was preceded in the same sense by London's Park Lane (1880). As a surname, Parker "keeper of a park" is attested in English from mid-12c. As a vehicle transmission gear, park (n.) is attested from 1949.
1812, "to arrange military vehicles in a park," from park (n.) in a limited sense of "enclosure for guns, wagons, horses, provisions, etc." (attested from 1680s). General non-military meaning "to put (a vehicle) in a certain place" is first recorded 1844. Related: Parked; parking. Park-and-ride is from 1966.