Jazz is built on very deep yet very simple structures - specifically, 4/4 swing rhythms, and circle-of-fifths harmony. I'll try to explain something of how swing rhythm works here, so you can grasp the depth of "slightly unpredictable repetitive" it offers, and the appeal of jazz (and its descendants, rock/country/R&B).
Swing is actually the simplest expression of a three-against-two polyrhythm. I don't know if this will format well on HN, but here's a try...
x-x-x-x-x-x-
x--x--x--x--
This is 12 subdivisions, divided into twos and threes. Where the twos and threes line up are interesting focal points. You can see them on the downbeat (start) and backbeat (middle). Now, let's try to express 3 against 2 in a lighter way...
| x--x-xx--x-x :||
or even
x--x--X--x-x
This last one is really interesting. The capital X (backbeat) is played with an accent to show a triplet-cycle lineup, and the trailing x is an "anticipation beat" into the next downbeat. With just those two things, you can express polyrhythm.
But unlike this notation, a beat isn't a fixed point in time! Rather, it's a region of probability where a sound might occur. Sounds can start anywhere in their beat, and attack or decay slowly or quickly, and evolve over multiple beats. This matters for the timekeeping instruments. Bass instruments tend to attack slowly, and high-pitched percussion like cymbals and snare drums attack very quickly. This creates a tension between the bass sense of time and the treble sense of time, tension that can be exploited musically.
So the backbeat and trailing anticipation beats that help define the underlying polyrhythm? They can be played early, or late. This can make the music feel faster or slower than it actually is!
Compare reggae and ska. They use exactly the same rhythmic structures. But in reggae, the guitar "skank" and the snare drum arrive very late, dragging the beat. In ska, they arrive early, pushing the beat. So reggae sounds relaxed, and ska sounds excited. Same beat, different meaning, just by manipulating the polyrhythmic emphasis.
The emphasis can also be manipulated by making the polyrhythm more or less explicit. Blues often has a very hard triplet feel. A lot of rock is very square and barely swings at all.
The beauty is that this is incredibly simple and repetitive, but offers an infinite variety of emotional expressiveness. This is why the American beat has dominated popular music for century. (As an aside, this is why so much drum machine music sounds painfully stiff - it lacks the core tool of expression)