What was the Jazz Age? How does this term has appear in "The Great Gatsby"?
The Jazz Age coincides with the setting of The Great Gatsby, but to my knowledge the term does not appear in the novel itself. It would probably be mentioned, though, in any preface or introduction.
'Jazz' in Webster's dictionary is 'music from blues and ragtime and marked especially by solo instrumental improvisation.' Historically speaking, this was a particularly euphoric period in American history marked by a rising nouveau riche (of which Fitzergerald himself identified) in the years preceding the Great Depression. It also was a time in which Negro music and its themes were assimilated into the mainstream.
Remember how the character Gatsby supposedly got all his money - from bootlegging during the Prohibition years. This would appropriately fix the time slot in the 1920s. From enotes Summary and Analysis, Chapter One:
The pursuit of this distorted American Dream leads to worship at unworthy shrines: beauty, youth, and pleasure become icons, gods unworthy of worship yet traceable as a quest as far back as Ponce de Leon, who searched for the Fountain of Youth. Resulting from the pursuit of these “ideals” are restlessness and unfulfilled lives. To reinforce this flawed concept and its effects, images of “restlessness” and “drifting” recur numerous times in the novel.
The musical improvisation characteristic of the Jazz Age corresponds well to this spirit of restlessness and entrepreneurship of an industrial era promising the moon but delivering Arpège.