"youth, lad; boy of the lower orders; personal servant," c. 1300 (early 13c. as a surname), originally also "youth preparing to be a knight" (beneath the rank of a squire), 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, with Century Dictionary, 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.