Fin de Siecle is French for "End of the Century." Although literally it could refer to the end of any century, it almost invaribly refers to the 19th Century. The term usually refers to the period preceding World War I, which brought about such radical cultural changes and rearrangement of the social order. Colloquially, the term usually suggests a decadent and naive golden age in contrast to the horror that followed.
A good introductory text on this period is Barbara Tuchman's The Proud Tower.