In the intro to notes we learned all twelve notes. When building scales and triads we always moved up and down in steps. The circle of fifths puts those steps into a handy diagram.
Starting with C at the top, each step clockwise jumps a perfect fifth ahead. The keys gain one sharp at every step.
Moving in the other direction adds flats instead. Every step is a perfect fourth away, which is the same as a fifth in the opposite direction.
Following these steps around the circle we pass through all twelve keys and finally return to C. The inner circle shows the matching minor keys.
Use the circle to quickly see how many sharps or flats a key has and which major and minor keys are related.