Where it helped me, John, was with getting to grips with jazz 'standards', because the popular songs on which much of mainstream jazz was based, use the same progression patterns - utilising the harmonic progressions in the 5ths cycle. Once I understand that, I could follow and improvise on those tunes, and get to grips with them more easily.

So, for example, many standards start on the tonic chord, drop down to somewhere on the circle and then work their way back round the circle to finish on the tonic. Once you 'get' this, it's immensely useful. "Sweet Georgia Brown" comes to mind - let's say it's in G...

Starts with a preliminary run down from G to E7, then goes to A7, then goes to D7 and back to G briefly - that's the first 8 bars, more or less. Well, that E7-A7-D7-G riff is right on the cycle and part of a cycle which goes:

G-C-F-Bb-Eb-Ab-Db-F#-B-E-A-D-G (choose whether you want chords written as sharps or flats). So, "Sweet G B" starts in G, drops down to E in the circle and works its way back through the succeeding chords to G. Et voila! Once that clicks, you're away and a jazzer (more or less)
:-)