The circle of fifths is generally used as a reference point for learning scales and key signatures; move clockwise to add sharps or move counter-clockwise to add flats.
Each of the 12 notes that surround the circle are derived from the overtone series, the frequencies that exist above a fundamental pitch. From a single fundamental pitch, the interval of a perfect fifth occurs as the second partial after the octave. That fifth becomes a new fundamental and then produces a fifth of it’s own. This cycle continues until it reaches back to the point where it all started; the results are easily visualized in a circle. The math behind this process is much more complex and doesn’t entirely add up, as nothing that exists in nature is absolutely perfect, but this is the basis for understanding why there are 12 notes in the western musical language; a starting point at least.
The circle keeps track of all the pitches and orders them into 12 notes separated equally by intervals of perfect fifths. Because their are several ways to treat the number 12, there are also other ways to group the notes that surround the circle: in groups of two’s, three’s, four’s, and six’s. From there, and through inversions, it’s possible to account for all the intervals that exist within the span of an octave.
The circle of fifths is also a guide for the principles of harmonic function. It provides structure for navigating the hierarchy that distinguishes one note from another, progressions from one chord to the next, and any modulation between neighboring key/tonal centers.