Never succeeded in grasping this concept
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In the simplest terms, I’ve always told my students that the circle of fifths is like the periodic table for music. It’s an arrangement of keys–or chords–in their most logical, musical connections to each other.
For example, if you’re playing a C major chord, the two chords that most naturally connect with it are F and G, the two chords on either side of C in the circle. This works with chords or keys or scales. The chord that sounds the “worst” or least natural–least connected–with C is the one furthest from it in the circle–F#.
If you happen to be in F# and you want to get to C, the easiest way to do it is to follow the circle F# B, E A, D, G, C. Each of those is a natural-sounding musical connection, so it will sound good all the way. (Or you could go the other direction: F# Db, Ab, Eb, Bb, F, C)
The more you play around with it, the more you see it everywhere. For example, probably the most famous jazz move is the ii V I chord progression. In the key of C, that’s Dm, G, C. So you could say it’s just three chords in a row on the circle–D, G, C, with the D chord as a minor chord. But then you also notice that Dm is the relative minor of F which is right on the other side of C. So, from another viewpoint, you’re playing F, G, C which is, again, three connected chords on the circle.
And, after a while, you begin to feel as though everything is connected into one sort of mega-chord and you start to go a little nuts and almost understand John Coltrane.
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