This piece was composed in Russia in the 1930s by Dimitri Shostakovich and despite its name it bears absolutely no resemblance with jazz music.
Russia was then under the Soviet regime, completely cut out of the rest of the world, unaware of the cultural and social developments taking place in other countries. This music was created in the spirit defined by the Soviet government and is more like a romantic valse. The name "jazz" in the title is most probably ironic and humorous.
For a classical composer, Shostakovich was very experimental by mixing many unusual instruments in the orchestra, such as saxophones banjo and Hawaiian guitar, as well as unusual music styles, such as waltz, polka and foxtrot. The outcome is an enticing dancing melody, but with some enigmatic side. This is probably the reason that "Jazz suite No 1" featured at Stanley Kubrick's last movie "Eyes Wide Shut" which is about an underground group practicing dark rituals.