"youth, lad, boy of the lower orders," c. 1300, originally also "youth preparing to be a knight," from Old French page "a youth, page, servant" (13c.), possibly via Italian paggio (Barnhart), from Medieval Latin pagius "servant," perhaps ultimately from Greek paidion "boy, lad," diminutive of pais (genitive paidos) "child."
But OED considers this unlikely and points instead to Littré's suggestion of a source in Latin pagus "countryside," in sense of "boy from the rural regions" (see pagan). Meaning "youth employed as a personal attendant to a person of rank" is first recorded mid-15c.; this was transferred from late 18c. to boys who did personal errands in hotels, clubs, etc., also in U.S. legislatures.