Generation is from Anglo-French and Old French generacioun (with many spelling variants) “line of descent; body of individuals born and alive at about the same time,” senses that first occur in the Vulgate (the Latin version of the Bible, prepared chiefly by Saint Jerome at the end of the 4th century). The French noun comes from Latin generātiō (stem generation- ), which in classical Latin means only “act of procreating, procreation.”
Generātiō is a derivative of generāre “to beget, father, produce, generate.” Generāre in turn comes from genus (stem gener- ) “race, people, nation, class, kind,” from the Proto-Indo-European root gen-, gon-, gnē-, gnō- (with still other variants) “to beget, give birth.”
Further Latin examples include gēns (stem gent- ) “family, race, nation, people” and nātiō (from gnātiō ) “birth of a child, issue; race, nation.” Gentēs, the plural of gēns, translates Hebrew goyim “nations” in the Vulgate. Gēns forms the Latin adjective gentīlis “belonging to the same family, race, or nation.” English gentile comes from the Vulgate usage of gentīlis “any or all of the non-Jewish nations” and later “heathen, pagan.” Proto-Indo-European gen-, gon- yields Greek génos “race, descent, descendant, child” and génesis “origin, birth.”
The naming of a generation of people characterized collectively by shared ideas, experiences, etc., dates from the 1920s, specifically, the automobile generation and the Lost Generation.

Did you mean regeneration?