Many people who start to play jazz notice a couple of significant differences chord-wise compared to traditional rock and blues. First of all, most chords have at least 4 notes, and their extras notes attempt to create leading tones that imply, through tension, the next chord. For example, typically in all genres, the 5 chord often is extended to make it a dominant 7 chord (with a flat 7) because it “leads” back to the 1 chord. G7 -> C.
In many jazz progressions, all the chords are 7th chords. The 1,4 chords becomes a Major7, the 2,3,6 chords become a minor 7, the 5 chord a dominant 7, and the 7th chord a diminished. It lends a more sophisticated sound as well as offering greater leading tones.
So what chords lead to what other chords? We already discussed how the 5 chord leads to the 1 chord, but the idea can be further extended. The 2 chord leads to the 5 chord, the 6 chord leads to the 2 chord and so on. So that many jazz and country jazz progressions will follow the pattern 3-6-2-5-1. In C that would be E-7 to A-7 to D-7 to G7 to Cmaj7.
If you know anything about the circle of fifths, you may recognize that pattern follows a 5 -> 1 movement. E.g. G to C is 5 -> 1, D to G is 5-> 1, A to D, E to A. So if we wanted to extend it by one more chord, we might use the 5 of E which is B. The B of course would be a B dim as mentioned already.
In many country jazz songs interestingly follow a lot of this idea, but keep the chords as simple 1-3-5 triads instead of the more jazzy sounding 4 note chords mentioned above. So you might hear a progression in a country song that squeezes in a 2 chord before going to the 5 chord. G to A to D back to G.
Also leading tones can explain how chords are altered in other ways, such as when the 4 chord is a simple folk or jazz song becomes the minor of that chord before leading to the 1 chord. This works because for the key of G the 4 chord is C major (C,E,G). Then when you turn it into C minor (C, Eb, G) which has a flatted third, it starts to imply a chromatic movement to the D note (E-> Eb -> D) the fifth of G. So many songs of the 50s and many Beatles songs feature a chord progression C -> Cminor -> G.
