Foliated art is loosely connected with the Arabesque. Arabesques in European art and Byzantine art are often decorative motifs comprising a flowing and voluted compositions featuring the acanthus plant. This served as ornamentation in architecture, in illuminated manuscripts, ceramics and in drawings and paintings. Foliated art appears in many other cultures e.g. the featured leaf work from Thailand above.
Simply, it is design in which the shape of foliage or leaf shapes play an important role either as a motif or as ornamentation in art. In popular usage, the term is neither so botanically specific not geographics specific and denotes all foliage appearing in some fine art or decorative arts context from across the globe. It goes a little in and out of fashion as well. In the art nouveau era organic flow of flowers, leaves and twigs were popular additions to the overall compositions of art. You can read more about art nouveau here.
