The basic elements are improvisation, syncopation, rhythm, blue notes, melody(the tune) and harmony(notes that fit well with the tune). Its structure is typically more complex than other popular forms of music. There is greater emphasis on the instruments used. They aren't in the background anymore. They form the heart of the song.
Tips to identify: Inability to follow the song. Lots and lots of bass. Incorporation of instruments you've never heard before like the sax. Did I mention bass?