The circle of fifths looks like a clock face filled with random letters. It is not random. It is a map of how the twelve keys relate to each other, and once you can read it, it answers a lot of questions at a glance.
What it shows
The twelve major keys are arranged in a circle. Moving clockwise, each key starts a perfect fifth (seven half steps) above the last: C, G, D, A, E, B, then F sharp, and so on back round to C. Moving anticlockwise goes down a fifth, or equivalently up a fourth: C, F, B flat, E flat.
Sharps and flats
Each step clockwise adds one sharp. C has none, G has one (F sharp), D has two (F sharp and C sharp), and so on. Each step anticlockwise adds one flat. F has one (B flat), B flat has two. That is why you can work out a key signature by counting steps from C.
Neighbours are close relatives
Keys next to each other share almost all their notes. C major and G major differ by a single note (F versus F sharp), so changing key between them sounds smooth. Keys on opposite sides of the circle share very few notes and feel far apart.
Relative minors
Every major key has a relative minor that uses the same notes. It sits three half steps below the major's root: A minor for C major, E minor for G major, and so on. Many circle diagrams show the minors on an inner ring.
Useful in practice
The three chords that belong together most often in a key (I, IV and V) sit in a row on the circle. In C that is F, C and G. This is why so many songs use those chords, and why moving round the circle by fifths is such a common chord progression.
My full guide has the diagram and worked examples: Circle of Fifths: The Complete Guide for Beginners.
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