"tract of level or undulating grassland in North America," by 1773, from French prairie "meadow, grassland," from Old French praerie "meadow, pastureland" (12c.), from Vulgar Latin *prataria, from Latin pratum "meadow," originally "a hollow," a word of uncertain origin; de Vaan suggests PIE *prh-to- "allotted."
The word existed in early Middle English as prayere, praiere, but was lost and reborrowed in 18c. from Hennepin and other French writers to describe the fertile but treeless parts of the American plains.
These are the gardens of the Desert, these
The unshorn fields, boundless and beautiful,
For which the speech of England has no name—
[William Cullen Bryant, from "The Prairies"]
Prairie dog for the burrowing rodent of the American grasslands, is attested from 1774, so called for its cry, which is like the barking of a dog; prairie schooner "covered wagon used by emigrants in freighting on the prairies and Great Plains before the construction of transcontinental railroads" is from 1841. Illinois has been the Prairie State at least since 1861. In Latin, Neptunia prata was poetic for "the sea."