A simple way of understanding why it is called the Circle of Fifths is by looking at a piano keyboard. Start at any key, count seven keys to the right (both black and white, not including the first) and you will land on next note shown on the circle.
Seven half steps, the distance from the 1st to the 8th key on a piano is a "perfect fifth" (“perfect” because it is neither major nor minor, but applies to both major and minor scales and chords; and a “fifth” because, although it is a distance of seven semitones on a keyboard, it spans five adjacent notes in the major or minor scale).
So, as you move around the Circle of Fifths in a clockwise direction, the next note you encounter will be a fifth above the note before it.
For example, starting with C, one fifth above C is G, which is the fifth note of the C major scale.
Next, we have D which is the fifth note of the G major scale.
Continuing on by fifths, we have, A, E, B, F♯, C♯, A♭, E♭, B♭, F, and finally C once again.
The same applies to the minor keys (on the inner circle). Starting with A Minor, E is a fifth up from A. B is a fifth up from E. F♯ is a fifth up from B. C♯ is a fifth up from F♯, and so on.