Art Nouveau's organic, undulating, rhythmic line was a deliberate attempt to uproot the imitative historicism that dominated much of the 19th century art.
Starting in the late 1880's, Nouveau emerged as a break with formal structured mathematical artworks - breathing organic life into what had become a disciplinarians endeavor to the Victorians. Prior to Art Nouveau a gold smith set stones into pieces which were - largely - rigid groups of circular, oval, or rectangular. Nouveau and subsequent eras birthed flowing shapes, pewter and enamel coating and floral motifs.
Period examples are plenty - in part because Nouveau is such a recent and collectible movement, and in part because Art Nouveau transcended borders; translations for the movement vary widely. We use the french term meaning New Art, the German Jugendstil translates to In the Style of Jugden [Magazine], the Spanish Arte joven to Young Art, and the Russian means Contemporary Art, but all describe the same movement.