"All That Jazz" is the opening number from the musical Chicago; the phrase had of course become a cliché long before Kander and Ebb came up with their award winning show and film.
The song is performed principally by Velma Kelly in a well choreographed scene in a jazz club. At the time this was set - 1924 - jazz hadn't been around for long, and was regarded by the more Puritanical as a corrupting influence, not the least because this was the era of Prohibition. As Velma performs she is unaware that the police have arrived to arrest her for murder. Velma Kelly was based on Belva Gaertner, who like the other principal female character in Chicago (Roxie Hart) was tried for shooting her lover dead. Both women were acquitted in spite of rather than because of the evidence.
Suggestion credit: Alexander Baron - London, England