Like the Arts & Craft Movement, Art Nouveau's intent was to break away from references to previous styles. However there is an essential difference between the two. Arts & Crafts relied on native, common materials, such as this oak chair;
Art Nouveau featured exotic, expensive materials, such as enamel and gold as executed by Lalique. 
Arts & Crafts was homey;
Art Nouveau, elegant.
The new style took its name from Siegried Bing's shop Maison de l'Art
Nouveau that opened in 1895 in Paris, a short lived gallery
featuring interesting French designs alongside Japanese furnishings. Many critics argued that Art Nouveau works were too expensive, featuring style over function, and therefore "not new". However, its legacy, particularly in the decorative arts remains strong.
Beginning in France & Belgium the movement uniquely expressed itself in places as diverse as Scotland, Austria & Germany, Spain & the U.S. Take the Tour on my Pinterest Board!
In France & Belgium the style relied on references to nature in its sensuous, flowing, organic forms. A distinctive motif included the whiplash curve. Alphonse Mucha, best known for his advertising & theater posters, featured feminine subjects emphasizing the movement of the whiplash curve & flowing tendrils (above). The sense of movement heightened by the advent of the motion picture & the freedom of women's rights are evidenced not only in Mucha's posters but by the fashion of Paul Poiret. 
An alternative style emerged in Glasgow Scotland; its ringleader was Charles Rennie Mackintosh, ("Mack") architect, furniture designer & artist. A seminal year for modernism,1900, had both its Paris World Exposition & Vienna Exposition. Mack was invited to participate with the more avant-garde Austrian architects rather than the French. Perhaps because of his artistic hand & the influence of his wife in the business, his style reconciles both feminine & masculine themes. A signature Mack motif is a stylized pink or purple rose.