What Is an Octave?
What Is an Octave?
An octave is the distance from a note to the next higher (or lower) note with the same name — A to A, C to C. It spans twelve half steps, and physically it's a doubling of frequency: the A at 440 Hz has octaves at 220 Hz and 880 Hz. Octaves sound so alike that music treats them as "the same note, higher or lower."
Octaves on the fretboard
The 12th fret of any string is exactly one octave above the open string — which is why the fretboard repeats there. More usefully, octaves make compact, movable shapes between strings:
From the low E or A string: two strings up, two frets up is the octave. From the D or G string: two strings up, three frets up (the B string's tuning quirk adds a fret). Chain those two shapes and one known note names three or four spots across the neck — the core trick behind finding any note fast, covered in depth in Octave Shapes on Guitar.