If you want to understand and appreciate jazz there is no better place to start—apart from listening to the music, of course—than with the critical writing of Nat Hentoff. Beginning in the 1950s when he was on the scene covering Monk and Miles, Clifford Brown, Charles Mingus, and any number of other giants, Hentoff has always written about the music and the culture in a way that makes it approachable for the outsider. Pick up records from that time and chances are Hentoff wrote the liner notes.
Take for instance this chapter on John Coltrane from Hentoff's wonderful book, Jazz Is. I think you'll dig it. (Also, while you're at it, I urge you to read Hentoff's memoir, Boston Boy, as well as the amazing book of oral histories, co-edited with Nat Shapiro, Hear Me Talkin' to Ya: The Story of Jazz by the Men Who Made It.)