Jazz is a style of music that is not much different from blues.  Some of the  instruments used in  jazz  include the saxophone and the piano; but the most common and classic of jazz instruments is the trumpet and other type horns.  There is not exactly a type of style in jazz as much as there is a way you have to play your instrument to play jazz.  As Nat Hentoff said, "The true jazz singer does not try to be a horn, but rather to phrase and glide and swing with the suppleness of a horn while not distorting or rushing or mashing the lyrics. . . it is the art of being a horn like singer rather than an artificial horn."
    Playing jazz includes a lot of improvising, where - while staying within the main beat of the song - the player makes up their own melody as they play, bringing a whole new turn in the way the music sounds.  Some of the most famous jazz singers are Billie Holiday, Louis Armstrong, and even Frank Sinatra is considered a jazz singer in some references.
    For more information on jazz and its performers, you should check out these books and sites:
    Listen to the Stories by Nat Hentoff