Looks pretty, but......
As your understanding of music theory grows the patterns in the cycle of 5ths become apparent.
To state the reasonably obvious, all notes of the chromatic scale are arranged so that they are a perfect 5th apart, and by using enharmonic equivalents (eg D flat = C sharp) they can be neatly arranged into a circle.
Premise - the strongest chord movements in traditional Western harmony are those in which the root of the first chord is a fifth higher than that of the chord it resolves on to.
We now have all notes (or chords) arranged a fifth apart so strong progressions (like ii - V - I) go anticlockwise around the cycle.
Related chords (and keys) are close together, distant ones are on the opposite side.
Find D. Lets call that the tonic, chord I, home base, the key we're in.
Move one step anticlockwise and you have G, the subdominant, chord IV.
Move one step clockwise and you have A, the dominant, chord V.
You now have all the chords you need for a "3 chord" song in D. Repeat for any other key you like.
If you move another step clockwise you get chord ii (E minor in this case), and another gives chord vi (B minor), which complete the "normal" set of chords you find in a major key in Western harmony. Why were ii and vi minor? (hence lower case) - we've got to look at scale structures to properly explain that.
That (for me) was the first use of the cycle of fifths, chord relationships within keys. Look more closely and you start to find other stuff, such as the order of keys, order of flats and sharps etc - but you don't need to buy a book for this, as there are plenty of good explanations on the web, starting with Pete's own theory section - I've pinched some of his explanations (thanks) for my teaching.