C major on the circle of fifths
Each step clockwise around the wheel moves up a perfect fifth and adds a sharp to the key signature, or takes a flat away. The small numbers around the rim show each key's signature. C major has no sharps or flats in its key signature.
Why the chords land where they do
The two rings work in pairs. Each minor key on the inner ring is the relative minor of the major key just outside it: the two are built from the same seven notes and share a key signature. C major and A minor are one such pair.
This pairing is why a key's chords gather in one place. Its three major chords, C, F and G (the I, IV and V), sit next to each other on the outer ring, each a fifth from its neighbour. Its three minor chords, Dm, Em and Am (the ii, iii and vi), are the relative minors of those same three, so they sit directly beneath them. Together, six of the seven chords form a block three wedges wide.
The remaining chord, B° (the vii°), is diminished. It sits four steps away from the block and is outlined on its own. Every major key, and every mode of the major scale, has exactly one diminished chord, and it is always the one that sits apart.
In this way the wheel works as a map of harmonic distance. Chords inside the block sound as though they belong to one key, and the further a chord sits from the block, the more it sounds like a departure. That is why progressions such as I–IV–V and ii–V–I move between neighbours rather than leaping across the wheel.
One step, on the neck
On the guitar, a perfect fifth is a shape you already know: the power chord. Play a root, then the note two frets higher on the next string up. Here it starts on C.
Now think of it as a chain. The G you are already fretting is the fifth of C, and it is also the root of the next chord clockwise. Play the same shape starting from G and you reach D. C → G → D is two steps around the wheel, and the same movement repeated up the neck.
The shape works here because these strings are a fourth apart. On the G–B pair the distance changes, so the fifth moves to a different fret. That is the one place this tuning breaks the pattern, and the reason familiar chord shapes change on the higher strings.
C major has no sharps or flats in its key signature. Six of its seven chords form one block on the circle of fifths.
Six of C major's seven chords sit together in one block on the wheel. The seventh, B°, sits apart.
If you arrange the twelve keys so that each one is a fifth above the last, they close into a circle, called the circle of fifths. The arrangement has a practical meaning. Neighbours on the circle share six of their seven notes.
C major and G major differ by exactly one note, because F becomes F♯. C major and F major also differ by one note, in the other direction, because B becomes B♭. That is why a song can move to a neighbouring key without sounding disjointed, and why the chords of a key sit together in one block of the circle rather than scattered around it.
The further apart two keys sit on the circle, the more different they sound. Keys on opposite sides share very few notes, so moving between them is the most distant change of key there is.