1) American style of music 2) King Oliver group 
A jazz band (jazz ensemble or jazz combo) is a musical ensemble that plays jazz music. Jazz bands vary in the quantity of its members and the style of jazz that they play but it is common to find a jazz band made up of a rhythm section and a horn section. The size of a jazz band is closely related to the style of jazz they play as well as the type...
Jazz band is London Cockney rhyming slang for a hand.
[n] - a small band of jazz musicians
jazz group noun a small band of jazz musicians