A brief lesson in jazz appreciation for non musicians:
1. Jazz is not simply about "making stuff up". In fact, a lot of it is reading and interpreting written music. In a big band like ours, interpretation is critical. For instance, two notes that are written to be of equal value are sometimes divided into 2/3 and 1/3 (rather then equally) in order to "swing". Also, notes can have a wide variety of brief markings on them: a dot, an upside down V, a horizontal straight line, a short squiggly line going sidewards, a longer squiggly line going down, a short comma after a note, etc. The key is to all interpret this together, typically following the lead player in each section.
2. The bass, piano and guitar ARE largely "making stuff up" (we call it improvising). More often than not, all they have is chord symbols like this: Cma7#11 or Eb13. From these symbols, the pianist and guitarist have to quickly figure out which notes to play - or not play - for each chord. Some chords last a while, while others can last less than 1 second. And the hardworking bass player not only has to read and understand the chord symbol, but he/she must find a note that fits the chord AND ensure that the series of notes produced makes some sort of logical sense. The drummer is listening to all of this, keeping time AND emphasizing what's going on in the rest of the band by playing simultaneous shot notes, or improvised drum "fills" when there's a period of silence. PLUS the drummer has to "set up" a major change in the music (like an upcoming loud part, or a change in the number of beats in the bar). And sometimes there are drum solos: some of which follow the pattern of the music, some of which do not. A good drummer will play something that clearly tells the rest of the band that he/she is coming to an end of the solo, and will lead into the next part.
3. Of course, if you are looking at a small jazz combo, all bets are off. Guitar, piano, bass and/or drums are improvising pretty much everything. There will typically be a rough sketch of the music (a one page simplified version of the melody with chords), but the musician playing the melody will almost never play it exactly as written - he/she will likely have their own interpretation. Following the melody, different people usually take improvised solos.Sometimes the order of the solos is pre-planned, other times one band member will give a subtle physical or musical signal to another when finished. And each member of the combo will interact with each other musically... sometimes a particular musical phrase will then be echoed by other players. That's one reason we close our eyes: to listen intently to the others. The end of the tune may be predetermined, or may be created on the spot by listening to each other and "setting up" a musically-logical and satisfying ending. And to go even further... I have even played gigs involving improvisation on music I've never seen before, with other musicians whom I have not even met prior to the gig.
Hopefully these points can give you more insight into what's going on in the band. Or you can forget all this, sit back or dance, and enjoy the music!